square by measuring diagonals - how accurate is accurate?

[Jesse Tutterrow]

A friend was helping me build a set of shop cabinets measuring 32" high (without the toe kick) by 30 inches wide. We started having a discussion about measuring the diagonals to check square. So, I thought I would ask your opinion.

Here is what we were discussing:

1. There will be a slight variation in measurement based upon what part of the end of the measuring tape is on the corner.

2. How close do the two measurements need to be in order to call the cabinet square? Within a 1/32nd? Or???

Thanks in Advance,

Jesse Tutterrow

[jared herbert]

There is always some spring back and movement after you take the clamps off, etc so it is hard to get them exact. I usually get them as close as I can in a minute or two, usually 1/16th and they seem to work just fine. You can straighten them up a little when you put the back on too, if it is cut square. Jared

[David Helm]

The measurements will be a accurate as your measuring tool is. Measuring diagonals is an old time honored method for squaring. If you are doing cabinets I would get them as close to zero variance as you can. If I were doing a foundation I would be happy with 1/16.

[Terry Beadle]

The square tolerance is directly related to the relationship of the cabinet and its surrounds. If it is to slide into a very square under counter situation, then you need to allow a 1/16th clearance on each side or use a hand plane to fit. The squareness of a free standing box or cabinet is not critical except to the eye. Humans can tell square very accurately when their attention is brought to the issue but usually if it's with in a 1/8th inch of square, that's not going to draw their attention. A picture frame is another matter.

If you are getting a 30 inch or larger cabinet within 1/32nd, you are gold IMO.

Dead square is a goal in a non-square world.

[pat warner]

Maybe for ball park impressions but for anything close to accuracy: A measurement with little value.
There are other and more accurate ways of determining squareness inside and out, not a vague opposite corner to corner guess with a rule that can't get into the corner itself! Don't count on it.

[Kyle Iwamoto]

1/16" for shop cabinets? You guys are good! I would not even measure....:eek:

[Jon Bonham]

Maybe for ball park impressions but for anything close to accuracy: A measurement with little value.
There are other and more accurate ways of determining squareness inside and out, not a vague opposite corner to corner guess with a rule that can't get into the corner itself! Don't count on it.

You'd be surprised how accurate it is, which is the reason it's been used for hundreds for years. The bigger the item you're measuring, the easier it is to use. Even minute variances will make for huge measurements differences on big items. For something small, it's probably easier to use a square.

[Mike Henderson]

Maybe for ball park impressions but for anything close to accuracy: A measurement with little value.
There are other and more accurate ways of determining squareness inside and out, not a vague opposite corner to corner guess with a rule that can't get into the corner itself! Don't count on it.
Uh, what would you do that's more accurate than a corner-to-corner measurement? I'm assuming an accurate and well fitting measurement device to measure the distances so my question relates to the technique itself and not some improved measuring device.

Mike

[Peter Quinn]

I'm with Kyle on this one. How accurate for shop cabs? Who cares, its not the opening for the door on the space shuttle. I'm making a set of shop cabs right now and come to think of it I didn't even check for square so much as one. I may have put a framing square in one corner to check for gross errors, thats it.

A nice way to check for square is with a shop made pinch stick. It lets you compare inside measurements in a real accurate fashion. Its making real accurate adjustments with clamps and plywood that has been glued and screwed that gets tricky. So the measurement may be dead accurate, but will the cabinets? I'm getting real good at scribing inset drawer fronts in less than perfect openings. That's really where the sum of all your errors comes back to bite you in the butt. Drawers of all kinds and inset doors like to operate in square openings. For over lay doors and applied drawer fronts. again, who cares!

[Will Overton]

I agree with Pat to a degree.The principal is dead on accurate, but the ability to measure exactly in the corner alludes some of our measuring devices.

In reality, if you do the math, you only need to measure one diagonal. Pythagoras proved that in a right triangle, A squared + B squared = C squared, where A and B are the sides and C is the hypotenuse (diagonal).

If you know your sides, top and bottom of your cabinet were cut correctly, the math has to work. If a cabinet is 3 feet wide and 4 feet high, the diagonals will both be 5 ft.

3² + 4² = 25

The square root of 25 = 5, so if your cabinet is square, both diagonals must equal 5 feet. If one of them is correct, the other one has to be correct. If one is wrong, so is the other.

[Lee Koepke]

I agree with Pat to a degree.The principal is dead on accurate, but the ability to measure exactly in the corner alludes some of our measuring devices.

In reality, if you do the math, you only need to measure one diagonal. Pythagoras proved that in a right triangle, A squared + B squared = C squared, where A and B are the sides and C is the hypotenuse (diagonal).

If you know your sides, top and bottom of your cabinet were cut correctly, the math has to work. If a cabinet is 3 feet wide and 4 feet high, the diagonals will both be 5 ft.

3² + 4² = 25

The square root of 25 = 5, so if your cabinet is square, both diagonals must equal 5 feet. If one of them is correct, the other one has to be correct. If one is wrong, so is the other.
The 3 -4 - 5 rule is how an old carpenter taught me as a teenager to verify that the batter boards / layout for our building foundations were square.

You can use any multiple of 3-4-5 to verify a square corner.

[Bill May]

measuring corner to corner is not accuratte at all if your peices are cutting correctly its just means your pieces are paralelle

[Gary Hodgin]

I don't know how close is close enough until it's too late. I try to get the stuff as square as I can. I'm always uneasy about using a tape measure especially on deeper drawers or cabinets. I now use a veritas bar gauge for most measurements. Recently, I ordered a couple of these "square checks" from Rockler, but haven't used them yet.

http://www.leevalley.com/US/wood/page.aspx?p=32585&cat=1,43513

http://www.rockler.com/product.cfm?page=18032

[Dave Lehnert]

measuring corner to corner is not accuratte at all if your peices are cutting correctly its just means your pieces are paralelle

What he said.
When I started woodworking I would struggle with this all the time. Your case would look out of square (because it was) but your diagonal measurements were the same. I had a hell of a time trying to get anyone to understand what I was trying to say.

[Cody Colston]

measuring corner to corner is not accuratte at all if your peices are cutting correctly its just means your pieces are paralelle

One has to assume a certain level of competency here...like the ability to cut pieces to the exact same length. It a person can't do that, the argument of how to check for square becomes moot.

Measuring diagonals is the accepted method...and has been for a long, long time. The acceptable tolerance will depend on the size of the cabinet.

My .02 - Just like everything in woodworking, strive for perfection and you may one day achieve excellence.

[Leo Graywacz]

measuring corner to corner is not accuratte at all if your peices are cutting correctly its just means your pieces are paralelle


What he said.
When I started woodworking I would struggle with this all the time. Your case would look out of square (because it was) but your diagonal measurements were the same. I had a hell of a time trying to get anyone to understand what I was trying to say.

If your measurements are equal for both your length measurements and both of your width measurements of your cabinet/board then your diagonal measurements will determine if your cabinet is square. I try to get all my cabinets within 1/64". Within a 32nd and I am still happy. 1/16" out of square is way to much.

[Bill May]

im not trying to start a argument but a parallelogram has equal corner to corner mesurements but is not square. people can do what they want but use a sqaure and corner to corner measurements( to compensate for unequal cut lengths) and u will be in the safe

[Ken Fitzgerald]

Bill,

I will take that argument.

Show me a drawing of a 4 sided object where the measurements from opposite corner to opposite corner are equal, the sides parallel and the corners are NOT square.

[Bill May]

http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Parallelogram.svg/255px-Parallelogram.svg.png (http://sawmillcreek.org/wiki/File:Parallelogram.svg)

[Ken Fitzgerald]

Bill,

A to C doesn't equal B to D.

[Jerome Stanek]

You drew the picture and they are not the same measurements. A 3X 6 parellelagram on a 45 has one measurment at 3.8787 and another at 8.1213 that is not the same.

[Steve Milito]

http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Parallelogram.svg/255px-Parallelogram.svg.png (http://sawmillcreek.org/wiki/File:Parallelogram.svg)

Assume ad=bc=3 and ad=bc=4

The only way for ac and bd to be equal would be if they were 5.
If that is the case then we have 3,4,5 triangles which means that adc and abc are 90 degrees

[Jon Bonham]

Let me restate, for emphasis. If your diagonals are the same, the rectangle is perfectly square. It's math, I'm not actually guessing here. I can prove what I say and I can prove what you say is wrong.

[paul cottingham]

If your measurements are equal for both your length measurements and both of your width measurements of your cabinet/board then your diagonal measurements will determine if your cabinet is square. I try to get all my cabinets within 1/64". Within a 32nd and I am still happy. 1/16" out of square is way to much.
I dunno. for me its a matter of percentage. 1/16 out over 1 foot is pretty bad. 1/16 out over 48 inches...not so much.

[Ken Fitzgerald]

Jon,

The key here is "opposing sides are parallel".

I can make a 4 sided object where two opposing sides aren't parallel and as a result, the corner to corner measurements will be equal but the corners won't be 90º.

[glenn bradley]

I use these. They reach into corners pretty well and have done the job for me.

[Jon Bonham]

Jon,

The key here is "opposing sides are parallel".

I can make a 4 sided object where two opposing sides aren't parallel and as a result, the corner to corner measurements will be equal but the corners won't be 90º.

Well, Ken, I honestly would have never even considered that as a possibility, since we're in a woodworking forum. ;) And since you're guaranteed to have no 90 degree angles on something with two matching diagonals and no sides the same length. :D

[Jon Bonham]

I use these. They reach into corners pretty well and have done the job for me.

Well, there you go. A really simple, elegant solution. Glenn, where did you get those?

[Brandon Weiss]

I don't know how close is close enough until it's too late. I try to get the stuff as square as I can. I'm always uneasy about using a tape measure especially on deeper drawers or cabinets. I now use a veritas bar gauge for most measurements. Recently, I ordered a couple of these "square checks" from Rockler, but haven't used them yet.

http://www.leevalley.com/US/wood/page.aspx?p=32585&cat=1,43513

http://www.rockler.com/product.cfm?page=18032

I have the rockler one. I like it, very simple and quick to use. I always check square corner to corner. It's the quickest way I know to check square. Sure, the math can be done ten different ways to check square but in these situations it's easiest for me to measure corner to corner. If you're worried about having a corner to corner measurement the same but not actually being square, you need to double check your pieces after you cut them. Why assemble something with inaccurately cut pieces? That's like wiping before you poop, makes no sense. I like to see my results within the accuracy of my tape measure. 1/32 if possible, but I'll take 1/16 if that's the tape I'm using. Accuracy can be a touchy subject here with some folks. For me, if it measures pretty close and I think it looks good, that's accurate enough. Some folks like to see and know more accuracy. Kind of like measuring your jointer bed to within 0.002". Unless I had a real problem with the boards coming off the jointer, I wouldn't worry too much about putting a dedicated straightedge up to my cast iron tables to check for flatness. But that's just me, others feel differently. Measure it, get it close, take a look, and if you like it, go for it. If not, adjust. Makes no difference if you're building shop cabinets or home cabinets, it's your project so get it where YOU want it.

[Steve Jenkins]

A couple people suggested that they are only shop cabinets.
I suggest that you always strive for perfection whether you are making shop, garage cabinets or fine furniture. The shop and garage stuff are perfect practice pieces to perfect your techniques. If you just bang things together then when it reallly matters you haven't had the practice you need to do quality work. When doing the shop and garage stuff you might decide that good enough is good enough but at least you're making a judgement call on the quality of that particular piece.

[Ken Fitzgerald]

Steve,

I agree. I always strive for perfection as it is good practice.

[Will Overton]

Jon,

The key here is "opposing sides are parallel".

I can make a 4 sided object where two opposing sides aren't parallel and as a result, the corner to corner measurements will be equal but the corners won't be 90º.

Only if one pair of opposing sides are not equal in length, or we need to rewrite the geometry books.

[Eiji Fuller]

A trapezoid has equal corner to corner measurements a parrallelogram does not. I dont think any of us are making enough mistakes to turn our rectangles into trapezoids so we're good.

Corner to corner measurements are plenty accurate enough. I like to get within 1/64th. For shop cabinets I just square up the cabinet with its square cut back and...

[Ken Fitzgerald]

Only if one pair of opposing sides are not equal in length, or we need to rewrite the geometry books.

Ah but if opposing sides are not equal in length, the other 2 sides are no longer parallel are they?

And we don't need to write new geometry books, we are coming to the same conclusion from different directions.

[Will Overton]

And we don't need to write new geometry books, we are coming to the same conclusion from different directions.

I'm pretty sure ...














... you are correct. :)

[Dave Lehnert]

One has to assume a certain level of competency here...like the ability to cut pieces to the exact same length. It a person can't do that, the argument of how to check for square becomes moot.

Measuring diagonals is the accepted method...and has been for a long, long time. The acceptable tolerance will depend on the size of the cabinet.

My .02 - Just like everything in woodworking, strive for perfection and you may one day achieve excellence.

You can cut all 4 boards to the same length but if the two boards that fit inside the other two are not cut 90 degrees on the ends, you get what Bill is trying to show.

Don't feel alone Bill, I know what you are talking about.

[Leo Graywacz]

90.00 degrees is very hard to achieve. Even with my square sled I can notice out of squareness if you cut two pcs and lay them on top of each other front to back.

[Carpenter Mark]

Of course cabinets-any cabinets (or any built object for that matter) should be square.
The easiest way to square cabinets, face frames, doors , drawers etc. , is with a rod (or beam) and trammel points. There’s no numbers to deal with or fractions to split- it’s either square or it isn’t. And if you use a set with eccentric points, it makes it easy to dial it in.

[Jon Bonham]

You can cut all 4 boards to the same length but if the two boards that fit inside the other two are not cut 90 degrees on the ends, you get what Bill is trying to show.

Don't feel alone Bill, I know what you are talking about.

Well then you're the only one. Because even if you have an angle <>90 degrees, if you set the diagonals equal and glue them up, they're square. PERIOD.

Honestly some of you guys are either not thinking this through or overthinking it in an attempt to rewrite the laws of geometry. IF you have two parallel pieces the same length and the other two parallel pieces the same length AND you have the same diagonal length THEN the rectangle is square. Now if you managed to cut your pieces with something other than a 90 angle on the mating edge, well then you'll have some sloppy looking joints, but it will still be square.

[Ken Fitzgerald]

Hey..........Let's chill out.

It is certainly not worth having a heart attack over.

Measuring diagonally from corner to corner has long been an accepted method of check squares, rectangles and yes, cabinets for squareness.

If it doesn't work for you, use what ever method with which you are comfortable and prefer.

[Steven DeMars]

Let me restate, for emphasis. If your diagonals are the same, the rectangle is perfectly square. It's math, I'm not actually guessing here. I can prove what I say and I can prove what you say is wrong.

I must say, some of you guys had me wondering . . . .

Just to check, I tried it in AutoCad . . .

IF IT IS "SQUARE" THE LENGTH FROM CORNER TO CORNER MUST BE THE SAME BOTH WAYS.

Steve:D

[Ken Fitzgerald]

I must say, some of you guys had me wondering . . . .

Just to check, I tried it in AutoCad . . .

IF IT IS "SQUARE" THE LENGTH FROM CORNER TO CORNER MUST BE THE SAME BOTH WAYS.

Steve:D

Yup!

It works for squares or rectangles.....

[Jesse Wilson]

You drew the picture and they are not the same measurements. A 3X 6 parellelagram on a 45 has one measurment at 3.8787 and another at 8.1213 that is not the same.


Agreed, someone needs to bring a Geometry book into the workshop..... :confused:

[Darrin Vanden Bosch]

Corner to corner is as accurate as you can get. It does not matter what measuring device you use as long as you use the same one for both measurements.

[larry cronkite]

And of course the fun begins when you install known square cabinets and the walls you install them on are not square!

[Kyle Iwamoto]

And of course the fun begins when you install known square cabinets and the walls you install them on are not square!

Oh now lets throw some gas on this already heated debate.... :D

This whole thread is pretty entertaining.....

[Thomas Bennett]

Quote:
Originally Posted by Bill May http://www.sawmillcreek.org/images/buttons/viewpost.gif (http://www.sawmillcreek.org/showthread.php?p=1484947#post1484947)
http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Parallelogram.svg/255px-Parallelogram.svg.png (http://sawmillcreek.org/wiki/File:Parallelogram.svg)

Assume ad=bc=3 and ad=bc=4

The only way for ac and bd to be equal would be if they were 5.
If that is the case then we have 3,4,5 triangles which means that adc and abc are 90 degrees


I'm confused! First ad=bc=3 and then change it to 4?
Do you mean ad=bc=3 and ab=dc=4??

[Ken Fitzgerald]

Oh now lets throw some gas on this already heated debate.... :D

This whole thread is pretty entertaining.....

That's why they invented caulk........or use of a compass.

[Jon Bonham]

And of course the fun begins when you install known square cabinets and the walls you install them on are not square!

There's the key. I challenge anyone to find a square wall in my house. :D

[Tony Bilello]

....cabinets measuring 32" high by 30 inches wide. ......Here is what we were discussing:

1. There will be a slight variation in measurement based upon what part of the end of the measuring tape is on the corner. This is correct. You must use the same measuring technique on both diagonals. Tony B
2. How close do the two measurements need to be in order to call the cabinet square? Within a 1/32nd? Or??? There is no reason to not get it right on the money. Tony B
Jesse Tutterrow

There are various techniques for squaring up. I just measure diagonally using a tape measure (on the outside). Then put a pipe clamp across the longer of the two measurements and close in on the measurements until they are the same. If for instance, one measurement is 40 1/4" and the other is 40", I know I have to split the difference and crank the longer diagonal to 40 1/8". Then re-measure again until both are exactly the same. This should take well under 60 seconds to get them both exact. For lower units, I recess the backs about 3/8" with a dado prior to assembly. Then take a 3/8" piece of plywood and square it to the exact dimensions of the inside of the recess and insert it in there - glue and nail or staple. If you cut a hair short, just keep it tight in one corner so everything is square. After glue dries, remove clamps. This is a very simple process.
For those of you that dont believe that exact diagonal corners makes an exact square, just do it by eye and dont worry. Nobody will ever notice the difference - maybe.

[Don Dorn]

I didn't take it as that heated and I'm learning allot about this.

[robert micley]

i have made a lot of cabinets. very few are perfectly square. but i have put a square in many top end cabinets in the face frames or inside with the square on the bottom or top . once again very few are dead on. it is almost impossible because to cut exact lenghts of plywood or rails and stile they would have to have zero warp- in another words they need to be dead flat. but you can get very,very close.

[John Mark Lane]

I just read thru this and my head is going to explode. I've been using corner to corner for more years than most of you have been alive. But one thing I learned from being a boat carpenter is, if you don't have something square to begin with, it doesn't much matter whether you can build something square to fit within it. The real skill is in making something that is not square, but fits.

Carry on.

[Dave Lehnert]

If I get some free time this week, I will get in the shop and make some cuts to show what I am trying to say.

Threads like this is good for the brain.

[Keith Outten]

Measuring diagonals is a perfectly acceptable means of inspecting your cabinet if it has 90 degree corners, which means it is a rectangle or square. The accuracy of your inspection is the result of the accuracy of the inspection tool and the technique you use.

How square your cabinet is involves the application of a tolerance. Ask any professional machinist.
.

[Sam Babbage]

Measuring diagonals is the best method of determining the squareness of an assembly. Clamping pressure can bow components making them read 'out of square' if tested with a square but the diagonals will give a true reading. Also, diagonals can be used to check 'non-square' assemblies, like a chair that tapers from the front to the back. In this case it is important that the angles are even, for fitting the seat, equal diagonals will ensure proper alignment.

To the people that use a clamp over the longer diagonal, of course that method works, but it is easier to just adjust the clamps that are already on the job. You simply make the clamps 'more parallel' with the longest diagonal.

As for the accuracy, it really is a matter of horses for courses. If I'm assembling a dining table, then 1mm or 1.5mm difference in diagonals would be perfectly fine. If I'm assembling a small carcass that will have inset drawers or doors then 0.5mm difference might be too much.

[Norman Hitt]

If I get some free time this week, I will get in the shop and make some cuts to show what I am trying to say.

Threads like this is good for the brain.

I understand what you are trying to say, HOWEVER, if the ends of the pieces you are trying to glue up are not SQUARE to the sides of those pieces, AND the lengths of the opposing sides are not exactly the same, they will never glue up square unless you leave gaps in the joint, in which case ANY method of measuring would be moot. Making all the pieces square just takes practice and attention to detail, no different than all the practice it takes to make a properly fitting dovetail. One poster said he couldn't get square ends even using his sled, but that only means that the sled needs tweaking of either the fence so it is 90* to the path of the cut OR the slop needs to be removed from the guide bar that fits in the slot in the saw table.

Please understand that I am not trying to be nasty, but just trying to point out WHERE the problem is, because diagonal measurement, (done properly) is the most accurate and easy method to determine squareness of a rectangle or a square and is the reason it has been used for centuries, think Pyramids.:D

[Marty Paulus]

Measuring diagonals is the best method of determining the squareness of an assembly. Clamping pressure can bow components making them read 'out of square' if tested with a square but the diagonals will give a true reading. Also, diagonals can be used to check 'non-square' assemblies, like a chair that tapers from the front to the back. In this case it is important that the angles are even, for fitting the seat, equal diagonals will ensure proper alignment.

To the people that use a clamp over the longer diagonal, of course that method works, but it is easier to just adjust the clamps that are already on the job. You simply make the clamps 'more parallel' with the longest diagonal.

As for the accuracy, it really is a matter of horses for courses. If I'm assembling a dining table, then 1mm or 1.5mm difference in diagonals would be perfectly fine. If I'm assembling a small carcass that will have inset drawers or doors then 0.5mm difference might be too much.
Oh boy Sam. Now you have thrown in the metric system! This is going to get even better now! :D Have to save this one for beers later.

[Lee Schierer]

A 1/32" is .03125". Assuming your opposites sides are exactly equal in length, if your 30 x 32 sides are off 1/2 degree, then your diagonal difference would be .382 or more than 3/8 of an inch. If you diagonals are different by 1/8 your sides are out of square .2 degrees.

I think getting within 1/16" should be close enough for most work.

[Steve Milito]

Quote:
Originally Posted by Bill May http://www.sawmillcreek.org/images/buttons/viewpost.gif (http://www.sawmillcreek.org/showthread.php?p=1484947#post1484947)
http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Parallelogram.svg/255px-Parallelogram.svg.png (http://sawmillcreek.org/wiki/File:Parallelogram.svg)

Assume ad=bc=3 and ad=bc=4

The only way for ac and bd to be equal would be if they were 5.
If that is the case then we have 3,4,5 triangles which means that adc and abc are 90 degrees


I'm confused! First ad=bc=3 and then change it to 4?
Do you mean ad=bc=3 and ab=dc=4??

Yes, sorry for the typo,

[Chris Kennedy]

If you have a triangle with sides a,b, and c, then the law of cosines gives you:


c^2 = a^2+b^2 - 2ab cos (C)


where C is the angle between the sides a and b, or equivalently it is the angle opposite the side c. If you have a parallelogram, then adjacent angles are supplementary, i.e. their sum is 180 degrees.

So, given a parallelogram like the one below
http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Parallelogram.svg/255px-Parallelogram.svg.png (http://sawmillcreek.org/wiki/File:Parallelogram.svg)

let t denote the angle ADC. Then the angle DAB is 180-t degrees. By the law of cosines:


DB^2 = DA^2 + AB^2 - 2(DA)(AB) cos (180-t)
AC^2 = DA^2 + DC^2 - 2(DA)(DC) cos (t)

Now, AB=DC, so we see that DB^2 = AC^2 (and thus DB=AC) if and only if cos(180-t)=cos(t) for some value of t between 0 and 90 (we may assume that the angle ADC is acute).

The cosine is positive for angles between 0 and strictly less than 90, and negative for angles strictly greater than 90 and less than 180. Moreover, the cosine is single valued in this range (i.e. no two distinct angles give the same value of cosine between 0 and 180 degrees). Therefore, the only way for the two diagonals to be equal is if 180-t=t, and thus t=90.

This is assuming Euclidean, i.e. plane, geometry. Also, it is an ideal situation. A line has an infinitesimal thickness, while when you are assembling boards, they are definitely not infinitesimally thick. So, there could be some wracking in the joint, warps in the boards, etc. that disturb this, but it cannot disturb it by much.

Cheers,

Chris

[Steve Griffin]

Here's a picture to show what may be causing confusion some here. As mentioned before you can measure equal diagonals and not have a rectangle, if the lengths are wrong.

Now before we hear yet again another scolding for shoddy workmanship, I would argue that this is the single most common cause for a cabinet to be out of square. If while cutting sides, top or deck, any of these 8 cuts is slightly off, (or any of the dados or partitions slightly off) then the length at the front of the cabinets will will differ. Its easy enough to make a nice square cabinet back, but the devil is in the other parts and operations, especially since multiple minor errors tend to work together not in your favor....

The benefit of checking diagonals/lengths, even for you claiming they have their tools all perfect and you yourself are perfect, is that it will quickly identify a problem. And even if you have built yourself a little trapazoid, equal diagonals will make it "as good as it will get".

-Steve

AD=CB and cabinet still sucks....

[Jim Summers]

The benefit of checking diagonals/lengths, even for you claiming they have their tools all perfect and you yourself are perfect, is that it will quickly identify a problem. And even if you have built yourself a little trapazoid, equal diagonals will make it "as good as it will get".

AD=CB and cabinet still sucks....


I think this says it all! :)

[Will Overton]

If you can't cut your boards correctly, you should work on that before worrying about square.

There are always if's.

If the dog didn't stop to take a poop, he would have caught the rabbit. ;)

[Ken Fitzgerald]

Here's a picture to show what may be causing confusion some here. As mentioned before you can measure equal diagonals and not have a rectangle, if the lengths are wrong.

Now before we hear yet again another scolding for shoddy workmanship, I would argue that this is the single most common cause for a cabinet to be out of square. If while cutting sides, top or deck, any of these 8 cuts is slightly off, (or any of the dados or partitions slightly off) then the length at the front of the cabinets will will differ. Its easy enough to make a nice square cabinet back, but the devil is in the other parts and operations, especially since multiple minor errors tend to work together not in your favor....

The benefit of checking diagonals/lengths, even for you claiming they have their tools all perfect and you yourself are perfect, is that it will quickly identify a problem. And even if you have built yourself a little trapazoid, equal diagonals will make it "as good as it will get".

-Steve

AD=CB and cabinet still sucks....

Steve,

And that is the very reason I stated early on that opposing sides have to be parallel.

Anybody can nitpick this to death but,

If it is a 4 sided object with opposing sides equal in length and parallel and the diagonal measurements are equal, the corners have to be square.

Period.

If you the angles of your cuts are poorly made, then the diagonals will not be equal due the skewing of the cuts and you won't have a square corner or "square" cabinet even if it's a rectangle.

[Ken Fitzgerald]

And now.....


Could we get a legal opinion on this?:confused::eek:

[Will Overton]

Steve,

And that is the very reason I stated early on that opposing sides have to be parallel.



And why back on page 1 I said;

"If you know your sides, top and bottom of your cabinet were cut correctly, the math has to work."

[Kyle Iwamoto]

If you cannot cut 2 boards reasonably the same length, and cut another 2 boards of another reasonably equal length, to make a frame that should LOOK somewhat square, perhaps you should find another job or hobby, because you will never make a square cabinet, no matter how you measure it. But then, given the fact that you cannot cut 4 pieces of wood, perhaps you cannot measure something properly in the first place.

But that cabinet MAY fit in my not square house.....:D

[Glenn Vaughn]

If you have a triangle with sides a,b, and c, then the law of cosines gives you:


c^2 = a^2+b^2 - 2ab cos (C)


where C is the angle between the sides a and b, or equivalently it is the angle opposite the side c. If you have a parallelogram, then adjacent angles are supplementary, i.e. their sum is 180 degrees.

So, given a parallelogram like the one below
http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Parallelogram.svg/255px-Parallelogram.svg.png (http://sawmillcreek.org/wiki/File:Parallelogram.svg)

let t denote the angle ADC. Then the angle DAB is 180-t degrees. By the law of cosines:


DB^2 = DA^2 + AB^2 - 2(DA)(AB) cos (180-t)
AC^2 = DA^2 + DC^2 - 2(DA)(DC) cos (t)


Now, AB=DC, so we see that DB^2 = AC^2 (and thus DB=AC) if and only if cos(180-t)=cos(t) for some value of t between 0 and 90 (we may assume that the angle ADC is acute).




The cosine is positive for angles between 0 and strictly less than 90, and negative for angles strictly greater than 90 and less than 180. Moreover, the cosine is single valued in this range (i.e. no two distinct angles give the same value of cosine between 0 and 180 degrees). Therefore, the only way for the two diagonals to be equal is if 180-t=t, and thus t=90.




This is assuming Euclidean, i.e. plane, geometry. Also, it is an ideal situation. A line has an infinitesimal thickness, while when you are assembling boards, they are definitely not infinitesimally thick. So, there could be some wracking in the joint, warps in the boards, etc. that disturb this, but it cannot disturb it by much.




Cheers,




Chris




If you look closely at the figure you drew you will notice the following:

1. Point A is to the right of a vertical line drawn from D.
2. Point B is to the right of a vertical line drawn from C.
3. Point A is closer to the imaginary vertical line drawn from C than B is to the imaginary line drawn from D.

It is impossible for the diagonals to be identical.
Draw the same figure on paper and measure.

I think this is what you said but got confused by the math.

[Ken Fitzgerald]

Kyle,

I will disagree with you.

Everybody starts out and I would dare say have projects with less than stellar results. It's typically part of the natural learning curve.

Have the courage to try something new. Strive for perfection while learning from your mistakes.

This board has beginners to Pros viewing and posting here. We can all learn from each other.

[Myk Rian]

70 posts to discuss square drawers? A new record perhaps.
I wonder what Sponge Bob Square pants would have to say about this. :D

[Steve Griffin]

And why back on page 1 I said;

"If you know your sides, top and bottom of your cabinet were cut correctly, the math has to work."

In that case, no need to check anything right?

I actually don't check every cabinet coming out of my shop, but ask my employees to during assembly.

-Steve

[Ken Fitzgerald]

70 posts to discuss square drawers? A new record perhaps.
I wonder what Sponge Bob Square pants would have to say about this. :D

Myk,

Might I suggest you need to change channels on your tv?

[Steve Griffin]

If you cannot cut 2 boards reasonably the same length, and cut another 2 boards of another reasonably equal length, to make a frame that should LOOK somewhat square, perhaps you should find another job or hobby, because you will never make a square cabinet, no matter how you measure it. But then, given the fact that you cannot cut 4 pieces of wood, perhaps you cannot measure something properly in the first place.

But that cabinet MAY fit in my not square house.....:D

I do do this for a living, and been building stuff for a lifetime and I still can't make a square cabinet.

I bet you can't either.

Here's what I would like to achieve someday--and do tell me if this is childsplay for you:

Build a kitchen of high end inset door cabinets with .050 gaps without test fitting the doors. Wouldn't that be nice? But guess what, with hundreds of parts and room for 1/64 errors here and there, I find I need to final fit each door to it's opening.

-Steve

[Will Overton]

In that case, no need to check anything right?



-Steve

No Steve. My original post included measuring the diagonal. In fact I was referring to only needing to measure one diagonal if you did the math first. My point here was simply that you had to start with boards that were cut to proper length.

[Matthew Hills]

Thought this thread was asking about measurement technique. Should be a worthwhile topic:

- I normally measure outside-to-outside, with tab of tape measure centered on the far corner (held by tension) and then I skew the tape so that the edge of the tape lines up with the opposite corner.

Two situations where this gets hard:
- work isn't a simple square, so the outside corners aren't accessible
- gets hard if a clamp is applied across the corners (having to work around the clamp/cauls/etc.)

Pinch sticks (as posted) are a good choice for measuring between interior corners. I just make mine on a temporary basis according to the size needed. I use a pair of spring clamps in the middle to hold the two pieces together. An alternative is to just hold the two sticks together in your hand and use a sharp pencil to mark the end of one on the other. Repeat for the other diagonal, and the difference in the marks is your error.

Just picked up but haven't used the tape tip from Lee Valley:
http://www.leevalley.com/US/images/item/Woodworking/MarkMeasure/50k5801s9.jpg

As others have mentioned, some preconditions:
- object is supported on a good surface
- pieces are cut to matched lengths
- pieces have not warped (plywood can too... grr....)

Matt

[Jon van der Linden]

A friend was helping me build a set of shop cabinets measuring 32" high (without the toe kick) by 30 inches wide. We started having a discussion about measuring the diagonals to check square. So, I thought I would ask your opinion.

Here is what we were discussing:

1. There will be a slight variation in measurement based upon what part of the end of the measuring tape is on the corner.

2. How close do the two measurements need to be in order to call the cabinet square? Within a 1/32nd? Or???

Thanks in Advance,

Jesse Tutterrow

A measuring tape will tell you something, though not really what you want. The traditional tool for this is two pieces of wood with pointed ends (so they fit into the corners) with some type of mechanism for holding them together. That way you can tell fairly accurately - it's not a question of numbers but of fit - it matches or it doesn't.

Even a small amount off can add up to big problems. Some people here are saying 1/16" is okay, it's not. When placing cabinets next to one another any error can be doubled, producing a significant gap. If it's perfectly square then it's good enough.

[pat warner]

"As others have mentioned, some preconditions:
- object is supported on a good surface
- pieces are cut to matched lengths
- pieces have not warped (plywood can too... grr....)

Matt "
********************************************
And if there is an error in your glue up, what do you do about it?
(& let's assume the thing looked square before you applied the adhesive, the "dry fit").

[Kyle Iwamoto]

I do do this for a living, and been building stuff for a lifetime and I still can't make a square cabinet.

I bet you can't either.


-Steve


I have already said that I can't make a square cabinet. The argument is that if you make a cabinet with 4 different length sides one can measure it to be exactly equal diagonal. The cabinet is not square. My point being that if you made a cabinet with shaped like a trapezoid, and measured it to be exactly the same corner to corner, what is the point? You need to find a different hobby. It's math. If the opposite sides are the same length, and the corner to corner measurement is the same, the cabinet is square. That has been done for centuries. I don't understand why people try to say that if the diagonals are equal, the cabinet is not square. It's math, it has to be. IF you assume that the saide are pretty much the same length.

[Ken Fitzgerald]

"As others have mentioned, some preconditions:
- object is supported on a good surface
- pieces are cut to matched lengths
- pieces have not warped (plywood can too... grr....)

Matt "
********************************************
And if there is an error in your glue up, what do you do about it?
(& let's assume the thing looked square before you applied the adhesive, the "dry fit").

You live with it.

[pat warner]

You live with it.
__________________
Ken
***************************************
And hence my point (tho not clearly stated) in the first place.
Namely, these measurements, no matter how heroic, vague, or precise, are done after the glue up where nothing can be done about it.

Moreover, a cursory inspection in the front of the cabinet, perhaps square, may not be in the rear of an 18" deep box. Panels sag.
A folly to chase, to be sure.

Can a measuring tool be rigid enough to inspect the hypotenuse of a 6' x 18" box? Can you hit the exact spot in each corner front and back?\
Can you read a 1/32 or a 1/64"? It just makes better sense to track the progress of your carcass as you proceed and to the best of one's desires, disposition and skillset.

[Keith Westfall]

A measuring tape will tell you something, though not really what you want. The traditional tool for this is two pieces of wood with pointed ends (so they fit into the corners) with some type of mechanism for holding them together. That way you can tell fairly accurately - it's not a question of numbers but of fit - it matches or it doesn't.

So a pinch stick on the inside is accurate but a tape on the outside isn't?

The center of the end of the tape on one corner and read the other end at the corner. Measure both the same way and you're good.

I'm thinking if I can see the difference in the pinch stick, I can also read the difference!

Something so easy into 5 pages so far.... :confused:

[Rick Christopherson]

It's very disheartening to hear the number of people say that they can't build a square cabinet, so why bother trying. It is this defeatist attitude that prevents you from achieving what is otherwise a very achievable goal.

Where does it begin or end? If your doors aren't square, why bother squaring the cabinet they fit into? If you can't make a square cabinet, then why bother squaring your saws to a high precision. If you can't cut two boards the same length, why measure to any degree of accuracy?

If you start your project with this defeatist attitude, you're going to finish your project defeated. I don't know about the rest of you, but I choose not to.

I can build a square cabinet, and I have on rare occasion even calibrated my sliding tablesaw down to 0.001 degrees when the project called for it.

You may not see the need to square, or check the square, on your projects, and that is your decision to make. However, if you are the type that is concerned about square, measuring diagonals is the fastest and most accurate method. That is where this discussion began, wasn't it?

[Steve Griffin]

It's very disheartening to hear the number of people say that they can't build a square cabinet, so why bother trying. It is this defeatist attitude that prevents you from achieving what is otherwise a very achievable goal.

Where does it begin or end? If your doors aren't square, why bother squaring the cabinet they fit into? If you can't make a square cabinet, then why bother squaring your saws to a high precision. If you can't cut two boards the same length, why measure to any degree of accuracy?

If you start your project with this defeatist attitude, you're going to finish your project defeated. I don't know about the rest of you, but I choose not to.

I can build a square cabinet, and I have on rare occasion even calibrated my sliding tablesaw down to 0.001 degrees when the project called for it. When some of us say we can't build a square cabinet, we are talking about things on a relative level.

You may not see the need to square, or check the square, on your projects, and that is your decision to make. However, if you are the type that is concerned about square, measuring diagonals is the fastest and most accurate method. That is where this discussion began, wasn't it?

Dude, you do not want me to come into your shop with precision equipment and check your work. You may think you have acheived absolute perfection, but I'm sure you haven't. The day I think I have, it's time to quit, because I'm deluding myself.

What we are discussing is all relative. When I say I can't build a square cabinet, I mean I can't build one perfectly square. I can build one square enough for a home depot style, overlay cabinet (like 90% of cabinetmakers build) without even paying attention. But some operations, like the precision required on some of my jobs, challenge me and my tools to the fullest extent.

When I was in boat building school, I had a teacher tell me something I will never forget. The difference between a beginner and a master is the master knows where to spend his time. A master knows how good is good enough. A master knows where to fuss about a 1/32 out of square, and when to fuss about a slight warp. The master knows what operations can be done with speed, and which need the utmost care.

The day I think I'm perfect is the day I'm completely done with this vocation.

-steve

[Matthew Hills]

It's very disheartening to hear the number of people say that they can't build a square cabinet, so why bother trying. It is this defeatist attitude that prevents you from achieving what is otherwise a very achievable goal.

Where does it begin or end?

is square over-rated?
http://blog.woodworking-magazine.com/blog/content/binary/500cabinetsp250.jpg

[Rick Christopherson]

Dude, you do not want me to come into your shop with precision equipment and check your work. Please don't be rude when you don't even know me. But yes, you can bring your precision equipment into my shop.

[Cliff Rohrabacher]

The bigger the cabinet the greater the accuracy of that method. It is a very reliable method.

[Joe Chritz]

Lets not forget that perfection is always an impossible goal. If my 18x42 upper cabinet door is .001 out of square that is extremely good accuracy. If my granite precision plate is .001 out of flat it is really bad.

It is all a matter of acceptable tolerances. Often the tolerances of a particular measuring tool are pretty large. The rule of ten says that a measuring tool must be accurate to at least ten times the tolerance involved with the construction. How many of use follow that for woodworking?

The tolerances used in normal wood construction would make a metal worker curl up and cry.

A tape is normal plenty accurate enough for measuring carcass construction as well as doors and drawers, etc. This assumes some care is used in consistent measuring technique. Even a digital caliper or micrometer requires good technique to get consistent results.

As already mentioned, spend your time worrying about what needs to be worried about.

Joe

[Lee Koepke]

Lets not forget that perfection is always an impossible goal. If my 18x42 upper cabinet door is .001 out of square that is extremely good accuracy. If my granite precision plate is .001 out of flat it is really bad.

It is all a matter of acceptable tolerances. Often the tolerances of a particular measuring tool are pretty large. The rule of ten says that a measuring tool must be accurate to at least ten times the tolerance involved with the construction. How many of use follow that for woodworking?

The tolerances used in normal wood construction would make a metal worker curl up and cry.

A tape is normal plenty accurate enough for measuring carcass construction as well as doors and drawers, etc. This assumes some care is used in consistent measuring technique. Even a digital caliper or micrometer requires good technique to get consistent results.

As already mentioned, spend your time worrying about what needs to be worried about.

Joe
not to mention that wood most likely will move a little in various unforeseen directions, even after glue up, backs on, etc .. ever so slight variation can create an unexpected 1/16th shift ...

[Will Blick]

Back to the OP issue of cabinet squareness via measurement....
If you measure a case you built, and compare the two measured diagonals, the diagonals are either of equal measurement, or they are of unequal measurement.

If the diagonals are of EQUAL measurements, AND, opposing sides are of equal length, you have one of the following:

1) You have a rectangle - (a parallelogram with 4 90 deg angles, opposing equal lengths, not equal to adjacent lengths)

2) You have a square - (4 equal lengths, 4 90 deg angles)

So with equal opposing side lengths, equal diagonals = 90 deg corners. PERIOD.


IF the diagonals are of unequal measurement, you have one of the following:

1) A Rhomboid Parallelogram - equal length opposite sides which are all parallel, but not at 90 deg angles. (a slanted rectangle)

2) A Rhombus parallelogram - a square that got slanted :-)


Now to further complicate matters, you can have unequal opposing lengths, in which now you no longer have a parallelogram. But if the goal is 90 deg corners, all you need is equal diagonals, it's either non equal lengths (which is easy to check) or unsquare clamping. For sanity, I always lay my opposing sides atop each other b4 glue-up. This confirms they are of identical lengths before gluing... Now I know for sure, unequal diagonals MUST = un square clamping.

The reason this method is so effective is because angle errors magnify over distance. So small angular errors can be measured with a low cost tape measure. For example, on a 32x48" rectangle, a 2/10 ths variance in diagonal measurement = nearly 1/2 a degree of angle error. It's much easier to measure 2/10 ths of an inch with a tape measure vs. trying to measure 1/2 deg with a low cost simple tool. This is the value of the LV and Rockler devices linked earlier. The accuracy of the tape measure is irrelevant, as long as you use the same tape for both diagonals.

For large cases, I dry fit on the floor, get equal diagonals and then draw pencil lines on the floor, now I don't need to be bothered re checking while I am in rush to get the clamps on.

[Ken Fitzgerald]

Will,

Your first statement isn't completely correct as written and for a reason you point out later.

You can have unequal opposings sides and if the centers of these opposing sides are centered with respect to each other such that a line drawn from the center of one of the opposing sides to the center of the other unequal opposing side is perpendicular to both and these opposing sides are parallel, their diagonals will measure identically and yet there won't be a single 90º angle in the four corners.

Will,

Check out post #62 in this thread and look at that drawing. If AE=FB Then CB =AD and yet there isn't a single 90º in the entire object.

[Ruhi Arslan]

measuring corner to corner is not accuratte at all if your peices are cutting correctly its just means your pieces are paralelle
Not accurate (no pun intended) at all. 1x1 square with equal length opposing edges being parallel gives identical corner to corner measurement. When the 1x1 square is distorted while maintaining the opposite edges parallel (parallelogram) , corner to corner distance changes. Only way the corner to corner will be equal on a parallelogram when it is no longer a parallelogram, i.e., opposing edges are not the same length which would not give you only one 90 degree corner anyway to begin with. I am confused too... :confused: :D

[Jon van der Linden]

So a pinch stick on the inside is accurate but a tape on the outside isn't?

The center of the end of the tape on one corner and read the other end at the corner. Measure both the same way and you're good.

I'm thinking if I can see the difference in the pinch stick, I can also read the difference!

Something so easy into 5 pages so far.... :confused:

It's not about seeing the difference.

With an out of square cabinet, if the stick is set to the larger diagonal it won't enter the smaller diagonal. Nothing to see, it just doesn't fit. If it fits in both with no movement, then it's dead on. It's very easy to detect differences as small as .001" by movement, reading a tape isn't even close.

When accuracy is required, a tape measure isn't the way to do it.

[Will Blick]

> Your first statement isn't completely correct as written and for a reason you point out later.

You can have unequal opposings sides and if the centers of these opposing sides are pependicular to each other and these opposing sides are parallel, their diagonals will measure identically and yet there won't be a single 90º angle in the four corners.


Ken, I re worded the post for clarity.... do you agree now? Once you try to wordsmith to shorten a post, you leave stuff out... I thought the word parallelogram covered your issue.

The key point I was trying to add to the thread was.... it's simple to confirm that opposing sides have the same length. (lay one atop the other) After you have that confirmed, the equal diag. measure test is a "slam dunk" to assure perfect (or near perfect) 90's.

IMO, this thread went off in a theoretical direction... since its a "build application", vs. a hypothetical application, we have the boards in front of us b4 assembling. Assuring equal opposing lengths eliminates all the remaining variables raised in this thread. (except thickness, warpage, etc. :-)

I guess the opposing side length check is the precuror to the diag. measurement check. Which as I explained above, is a VERY reliable method to assure near perfect 90's. with minimal effort.

[Will Blick]

> When accuracy is required, a tape measure isn't the way to do it.


The story stick is the best of all measuring devices... no reading required. As you suggest, we can feel a few thou of movement. However, IMO, it's more applicable (or practical) with small boxes, where the angle errors do not have the length to magnify.

I mentioned above, how 2/10 ths of an inch on an avg. size cabinet box = .5 deg error. We can all easily read down to 1/16th of inch on a tape measure, which is .15 deg angle error. 1/32nd, if you have decent eyes will get you down to .07 deg angle error... I would think .15 deg angle error is considered a success in ww.

[Ken Fitzgerald]

Will,

I will agree there is often a difference between theory and practice.

In my shop, I try to get as close to perfect as I can within reason.

The measuring of diagonals is a perfectly acceptable method of measuring squares and rectangle for squareness.

If anyone wants to use a different method, and it works for them, go for it.

But in theory and in general practice, using a tape measure and measuring diagonals is acceptable.

Use what works for you consistantly.

[Larry Feltner]

http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Parallelogram.svg/255px-Parallelogram.svg.png (http://sawmillcreek.org/wiki/File:Parallelogram.svg)

Maybe I am confused myself, but I think what he is trying to say is that if you have two sides, both of which are parallelograms, then if you measure from side 1A to side 2C, it will be the same distance as when you measure the opposite diagonal of side 1C to side 2A. However, measuring just 2 diagonals will not tell you if you are square. Side 1B to side 2D, and side 1D to side 2B must also equal the diagonal measurements of the other 2 diagonals. In the case of a parallelogram they will not.

[Nathan Yeager]

What he said.
When I started woodworking I would struggle with this all the time. Your case would look out of square (because it was) but your diagonal measurements were the same. I had a hell of a time trying to get anyone to understand what I was trying to say.


I don't understand this in the least. You are saying that your pieces are the correct dimensions, are appropriately parallel, and have matching diagonal angles yet they are out of square?

I only have a math minor, so I could be persuaded otherwise, but this seems doubtful. Could you explain?

[Ken Fitzgerald]

Maybe I am confused myself, but I think what he is trying to say is that if you have two sides, both of which are parallelograms, then if you measure from side 1A to side 2C, it will be the same distance as when you measure the opposite diagonal of side 1C to side 2A. However, measuring just 2 diagonals will not tell you if you are square. Side 1B to side 2D, and side 1D to side 2B must also equal the diagonal measurements of the other 2 diagonals. In the case of a parallelogram they will not.

Larry,

Take a piece of paper, use it to mark the length of one diagonal and compare it to the other diagonal on the drawing you posted. The diagonals ARE NOT equal in length. Thus none of the angles are 90º.

Mathematically, if the opposite sides of a 4 sided object are parallel, equal in length and the measurement from opposite corner to opposite corner are equal, all 4 corners of the object will and must be 90º. Period.

[joe milana]

.........................................

[Dave Lehnert]

.........................................

Just would like to know if the OP ,Jesse, got his cabinet built. LOL!!!!

[Harold Burrell]

1/16" for shop cabinets? You guys are good! I would not even measure....:eek:

Yeah, right...

I figure that if it doesn't tip over when it's finshed then it's a job well done!

[Larry Feltner]

Larry,

Take a piece of paper, use it to mark the length of one diagonal and compare it to the other diagonal on the drawing you posted. The diagonals ARE NOT equal in length. Thus none of the angles are 90º.

Mathematically, if the opposite sides of a 4 sided object are parallel, equal in length and the measurement from opposite corner to opposite corner are equal, all 4 corners of the object will and must be 90º. Period.

Ken, I agree with you, but that was not what I was saying. Yes in the diagram posted line a-c and b-d will not be the same length, therefore, the 4 sided object is not square. I think the poster who posted this diagram was saying something entirely different. I don't think he is measuring the diagonals of the sides of the box to determine squareness, but the diagonals of the box (opposite corner to opposite corner) once constructed. Read carefully what I was saying. When building a box you have 4 sides. Lets start by saying 2 are parallelograms and 2 are square. The 2 parallelograms are the opposite sides and they are joined together by 2 square sides. In this case if you measure from side 1(a) to side 2(c), and then from side 1(c) to side 2(a), you will get the same measurement. However, if you are measuring that way to see if the box you built is square, 2 measurements aren't enough. You also have to measure one of the other 2 diagonals. You have to measure from side 1(b) to side 2(d). If the box is square that measurement will match your first 2. In this case it will not because two of the sides were cut as a parallelogram. That is the only explanation I can come up with for what he is trying to get at.

[Caspar Hauser]

Ken, I agree with you, but that was not what I was saying. Yes in the diagram posted line a-c and b-d will not be the same length, therefore, the 4 sided object is not square. I think the poster who posted this diagram was saying something entirely different. I don't think he is measuring the diagonals of the sides of the box to determine squareness, but the diagonals of the box (opposite corner to opposite corner) once constructed. Read carefully what I was saying. When building a box you have 4 sides. Lets start by saying 2 are parallelograms and 2 are square. The 2 parallelograms are the opposite sides and they are joined together by 2 square sides. In this case if you measure from side 1(a) to side 2(c), and then from side 1(c) to side 2(a), you will get the same measurement. However, if you are measuring that way to see if the box you built is square, 2 measurements aren't enough. You also have to measure one of the other 2 diagonals. You have to measure from side 1(b) to side 2(d). If the box is square that measurement will match your first 2. In this case it will not because two of the sides were cut as a parallelogram. That is the only explanation I can come up with for what he is trying to get at.

Burble Burble... Conic sections next please! :)

[Will Blick]

> When building a box you have 4 sides. Lets start by saying 2 are parallelograms and 2 are square.


Larry, by definition, a parallelogram is a four sided structure. I think your posts may be using wrong terminology, making it hard to understand your point?

[Glenn Vaughn]

Ken, I agree with you, but that was not what I was saying. Yes in the diagram posted line a-c and b-d will not be the same length, therefore, the 4 sided object is not square. I think the poster who posted this diagram was saying something entirely different. I don't think he is measuring the diagonals of the sides of the box to determine squareness, but the diagonals of the box (opposite corner to opposite corner) once constructed. Read carefully what I was saying. When building a box you have 4 sides. Lets start by saying 2 are parallelograms and 2 are square. The 2 parallelograms are the opposite sides and they are joined together by 2 square sides. In this case if you measure from side 1(a) to side 2(c), and then from side 1(c) to side 2(a), you will get the same measurement. However, if you are measuring that way to see if the box you built is square, 2 measurements aren't enough. You also have to measure one of the other 2 diagonals. You have to measure from side 1(b) to side 2(d). If the box is square that measurement will match your first 2. In this case it will not because two of the sides were cut as a parallelogram. That is the only explanation I can come up with for what he is trying to get at.

Short form (I think):

To ensure the cabinet is square in all dimensions you need to measure the diagonals on more than one side.

[Larry Feltner]

> When building a box you have 4 sides. Lets start by saying 2 are parallelograms and 2 are square.


Larry, by definition, a parallelogram is a four sided structure. I think your posts may be using wrong terminology, making it hard to understand your point?

I agree that this is difficult, and maybe impossible, to explain on a message board. On top of it all, it may not even be what the poster intended, just my guess. A parallelogram is a two dimensional structure, i.e., the board that makes up one side of a box. It is not 3 dimensional, such as a parallelepiped. The cabinet is a 3 dimensional structure, in my example, made up of two parallelograms on each end joined by square boards on each side. I think the poster who posted the diagram of the parallelogram is measuring from diagonal corners across and through the inside of the cabinet. In other words, I don't think he is measuring along one side, but from opposite corners through the cabinet. If one parallelogram side is side 1 and the other is side 2, he is measuring from side 1(a) to side 2(c), and then from side 1(c) to side 2(a). This will give the same measurement but it is inadequate if you're measuring in this way. You also have to also measure side 1(b) to side 2(d). I think this is where his confusion is coming from in thinking that measuring diagonals doesn't work, but it's just my guess. The a,b,c,& d is in reference to the labels on the parallelogram posted by another poster, which has since been lost in these replies.

[Mark Woodmark]

Asumming the cabinet width is identical top and bottom, I strive for plus or minus 1/32 inch. Also, I always measure using the same edge of the tape measure and the same spot on this tape measures hook. Be sure to pull the tape tight as the hook always has some play in it

[Chris Padilla]

Larry,

OK, I finally GOT what you are saying. I think for the most part, people just measure the 2D "face" square/parallelogram and if the diagnols are close, we're happy. I've NEVER EVER considered measuring from the face of one corner (cabinet front) to the back of the opposite corner (cabinet back)--measuring "through" the cabinet as it were....

BUT, perhaps that is what the OP was doing...I dunno. :)

[Larry Feltner]

Larry,

OK, I finally GOT what you are saying. I think for the most part, people just measure the 2D "face" square/parallelogram and if the diagnols are close, we're happy. I've NEVER EVER considered measuring from the face of one corner (cabinet front) to the back of the opposite corner (cabinet back)--measuring "through" the cabinet as it were....

BUT, perhaps that is what the OP was doing...I dunno. :)

Chris, I agree. I'm not sure how you would even measure accurately through the cabinet across the diagonal. But that was the only thing that made sense to me that he was trying to explain. Maybe I am way off but if he is measuring along the side what he says doesn't make any sense. At least not to me.

[Ken Fitzgerald]

I work with twp planes at a time in my shop.

At work, work, I work with 4 planes at time....X....Y.....Z....time.

[Chris Padilla]

I use my block plane, jointer plane, smoothing plane, and my edge-trimming plane. :D

[Ken Fitzgerald]

Chris....you left out the SMC corporate "jet plane".

Is it your turn or mine?

[Jim Rimmer]

Assume ad=bc=3 and ad=bc=4

The only way for ac and bd to be equal would be if they were 5.
If that is the case then we have 3,4,5 triangles which means that adc and abc are 90 degrees
You hit it there. The Pythagorean method works IF it is a right triangle. If it's not 90 degrees in the corner (i.e, square) then your diagonal measurement will be off.

[george wilson]

Did anyone mention that they use the diagonal measuring system in the cabinet maker's shop in Williamsburg? Mack Headley and his staff use it. Even the house wrights use it.

[Leigh Betsch]

Agreed, someone needs to bring a Geometry book into the workshop..... :confused:

Stop this crazy talk!:eek: This woodworking stuff is supposed to be fun!;) Course it might coming in handy for hold'n veneer down flat....

[Leo Graywacz]

This is not some theory. It is a matematical proof. There is no doubt that this works. It has been proven my matemetical geniuses. If it doesn't work for you.....well....it must be you. :rolleyes:

[Kent A Bathurst]

Well......I just glued up the first of two garden gates: 31" x 51", made from ~3x5 WRC for the stiles and rails. Two 1x8 WRC as verticals in the center, matching the pickets in the adjacent fence.

Corner-to-corner diagonals are off by nearly 3/64". :eek:

I guess I could use the jointer to shave it to square, or maybe buy that LN #7 I always wanted. Or - maybe I should just cut it up and start over?

Heading for my foxhole now.......:D:D:D

[Will Overton]

Heading for my foxhole now.......:D:D:D

No need to duck and cover, they're your gates. Why should anybody else care if they are square or not. :D

[Kent A Bathurst]

No need to duck and cover, they're your gates. Why should anybody else care if they are square or not. :D


Better'n that - they're my neighbor's gates, WIll.

[Will Overton]

Better'n that - they're my neighbor's gates, WIll.


http://www.runemasterstudios.com/graemlins/images/roflmao.gif

[Kent A Bathurst]

No need to duck and cover, they're your gates. Why should anybody else care if they are square or not. :D

Will - second of 2 gates in the clamps. Thanks to your encouragement, I got this one into the barely acceptable range - just under 1/64" out of square via diagonals measurement.

I decided I'll just tell the neighbor he must be drunk when he comments on the parallelogram of the first one.

However - I didn't have the "fortitude" to read all 8 pages of posts on this thread, but the few I did scan lead me to think there is a chance that this method won't tell me if they are square?? Something to do with string theory, effect of rotational dynamics of the earth on long wood fibers, and tin foil hats, I guess.

Heck with it - they ain't my gates anyway.:D:D