Stupid math question of the day.

[Rich Engelhardt]

Hello,
I want to make a 6 sided box.
What angle do I set the saw blade at?

[Matt Ocel]

30 - I believe

360 / 6 = 60
then
60 / 2 = 30,

[Jim Fox]

Hello,
I want to make a 6 sided box.
What angle do I set the saw blade at?
Just ran a hexagon on sketchup.......and yes, the miter angle you'd need is 30°.

[Anthony Whitesell]

FYI the calculation is as follows:

360 divided by the number of sides then divided by 2.

360 = degrees in a full circle.
number of sides in the box (self explanatory)
2 because you take half the cut from each end from each piece (ie., twice as many cuts as you have sides)

[Tim Thomas]

The formula for finding the sum of the interior angles of any regular n-sided polygon is:

180 * (n - 2) where n is the number of sides

Therefore, to find the sum of the interior angles of a hexagon (six sided)...
180 * (6 - 2) =
180 * (4) =
720

Then divide by the number of angles to find measure of a single angle...
720 / 6 =
120

So the measure of each interior angle on a hexagon is 120 degrees. If you want to create simple mitered corners you will need to cut this measurement in half and set your saw blade at 60 degrees.


Reference:
http://www.mathreference.com/geo,iap.html

[William OConnell]

So the measure of each interior angle on a hexagon is 120 degrees. If you want to create simple mitered corners you will need to cut this measurement in half and set your saw blade at 60 degrees.


Hmm its actually 30. Rarely will you find a saw with the capabilities of cutting a 60 degree angle
But then again if you cut at 30 you have 60 left out of a squared 90 end
Ive become quite proficient at taking my architects complicated autocad math calculations and translating them into Carpenterese
He says 71 I hear 19
He says 63 I hear 27
He says 146 I hear 34 etc

[Anthony Anderson]

Rich, Matt and Anthony did a nice job of explaining it. Bill

[Montgomery Scott]

Tim's formula is the wrong one to use for what you want. This formula describe the angle between two adjacent sides of a polygon, not the interior angle measured at the center of a polygon.

As has been stated above the interior angle at the center of a polygon is 360 deg/n sides. The cut angle is then half of the resultant.

[Chris Padilla]

The formula for finding the sum of the interior angles of any regular n-sided polygon is:

180 * (n - 2) where n is the number of sides

Therefore, to find the sum of the interior angles of a hexagon (six sided)...
180 * (6 - 2) =
180 * (4) =
720

Then divide by the number of angles to find measure of a single angle...
720 / 6 =
120

So the measure of each interior angle on a hexagon is 120 degrees. If you want to create simple mitered corners you will need to cut this measurement in half and set your saw blade at 60 degrees.


Reference:
http://www.mathreference.com/geo,iap.html

Tim,

While this is correct for finding the "sum of the interior angles of a polygon", that is not what we are trying to accomplish here. You don't use the interior angle...you use the angle measured from the center of the polygon...or the exterior angle, which is 180 minus the interior angle.

[Tim Thomas]

Given the very limited information in the original post, here is what I assumed Rich wanted to do:

"I want to make a hexagonal box"

This to me means: "I want to make a box that when I look down at it from the top I see a hexagon. I want to create mitered corners for the joints. When I cut the sides for the box, what angle should I miter the edges at so when I join all of the pieces up it makes a hexagonal box?"

If I were to make such a box myself I would tip the saw blade of my tablesaw to 60 degrees and cut all the sides from a single long piece of stock. You could quickly make all of the sides by trimming the end to 60 degrees, then flip the board over, slide it to a predetermined stop and cut a side. Then flip again, slide and cut, repeat this 5 times and you should have six pieces of equal length that have 60 degree miters on each end that will make the sides of a perfect hexagonal box.

First attached image is of the assembled sides viewed from the top down. Second image shows the cut lines on a single long piece of stock when viewed from the edge that would make all of the side pieces. Third image shows a way to get better grain "flow" around the outside of the box by alternating the 60 degree cuts. Would take longer to cut this way, but grain matching might look better.

[Anthony Whitesell]

But you can't tip the saw to 60 degrees per se. The scale only reads 0 to 45. Therefore you need to cut based on the 'other' angle (30 instead of 60). Our formulas calculate the same cut based on the 'other' angle.

[Chris Padilla]

Remember that angles are always with reference to something else.

This often confuses woodworkers in deciding that if a TS blade straight up perfectly perpendicular to the table top is at 0 degrees or 90 degrees. Keep in mind that most adjustments are only a total of 45 degrees so anything greater than that and one usually must reorient the work to cut at the "90 minus what you want" degrees.

[Tim Thomas]

But you can't tip the saw to 60 degrees per se. The scale only reads 0 to 45. Therefore you need to cut based on the 'other' angle (30 instead of 60). Our formulas calculate the same cut based on the 'other' angle.

Agreed: when the scale reads 30 degrees the angle of the blade relative to the surface of the table saw will be 60 degrees. The angle of the blade relative to the vertical surface of the fence would be 30 degrees. I've never really understood why they use the angle of the blade to the surface of the fence as the reference and label it "0 degrees". It seems that I am much more often moving a piece of stock with its widest surface down on the table top, rather than up against the fence. The only time I make that kind of cut is for raised panels, which isn't very often at all really. I like to think in terms of the angle of the blade relative to the table surface, but it all works out the same anyway.

[Alan Schwabacher]

That's one of the nice things about the wixey (or beall) angle measurement of blade angle: if you zero it on the table and read at the blade, it gives you the actual angle you cut, rather than 90 - the angle that the saw reads. It may seem like a straightforward thing, but it did create some confusion here.

[Frank Drew]

I think the others have answered the original poster's question quite well. As an aside... years ago Bridge City Toolworks sold an inexpensive pamphlet that gave you blade tilt and miter gauge angles for any number of multi-sided, variously angled boxes, hoppers, bins, whatever. A terrific reference if still available.

[Tom Veatch]

... I've never really understood why they use the angle of the blade to the surface of the fence as the reference and label it "0 degrees". ...

If you think of it as the "angle off square", then blade tilt and miter angle has the same definition. 0° is a square cut and 30° is "30° off square" for both miter and tilt. Don't know if that's why they're defined that way, but it seems to make sense to me.

[Rich Engelhardt]

Hello,
Thanks!

I *think* I have it.
I was using the formula Tim listed and was coming up with figures that didn't make sense to me.

So - to sum it up - if I set my blade @ 30* and rip each both edges of a piece of wood 3" wide - then cut off 6 pieces 5" long and put them together, I'll have a 5" high six sided box (w/out a top or bottom of course @ this point).

That makes sense - I guess- I'm still fuzzy about the "other angle", but I guess it'll sink in at some point.

I did make an 8 sided base once and recall I set the miters for 22.5* - so - 30* for six sides sounds reasonable enough to give it a try.

[Matt Ocel]

Rich -

post pics for us

[Jason Roehl]

I guess we could all think of it this way: a miter saw is a crosscut saw, so a perfect 90º cut would be 0º from normal, and the 60º cut the OP needed is 30º from a perfect crosscut, not the fence.

[Rich Engelhardt]

Hello,
Doh!

After turning this over in my head for a few days, a light suddenly went off and I see it clearly now.

Take a 12" pizza, cut it into 6 equal pieces, trim the crust off so the ends are straight - then I end up with a 12" six sided pie.

If I take it a step farther, and cut off 5" from each piece - starting at the pointy end measuring towrds the flat part left by the above cut off crust, I end up with a 10" six sided pie and a 12" six sided donut (or box).

The angle I want - 30* is what each side of the slice of pie & each side of the pieces of donut are.

Made perfect sence once I extened each side to a point in the middle.


Matt,
Wiill do.
The "box" is really a six sided bird feeder project my grandson is doing for cub scouts. I ran across a picture of one at a craft web site. It looks like it should be simple enough to make one similar to it.

[Myk Rian]

If you want a 60deg angle, cut at 30deg. When the parts are put together, you have 60.
I make 8 sided light houses, and use a 22.5deg bit in my router table to bevel the side pieces. 22.5 x 2 = 45.
To make the tapered sides, I use an angle jig.

[Thomas Williams]

Well, I am not sure about all the math formulas, so if I want to cut a multi sided project, I look at the quick reference angle chart on my Incra miter gauge. 6 sides would be 30 degrees. I also use to have a program for segmented turning that would give you the cut angle.

[Thomas Knighton]

It's funny how much discussion went into this "stupid" math question, isn't it? ;)

I think it's safe to say it wasn't all that stupid to begin with.

Tom

[Mark Rios]

Hello,
Doh!

After turning this over in my head for a few days, a light suddenly went off and I see it clearly now.

Take a 12" pizza, cut it into 6 equal pieces, trim the crust off so the ends are straight - then I end up with a 12" six sided pie.

If I take it a step farther, and cut off 5" from each piece - starting at the pointy end measuring towrds the flat part left by the above cut off crust, I end up with a 10" six sided pie and a 12" six sided donut (or box).

The angle I want - 30* is what each side of the slice of pie & each side of the pieces of donut are.

Made perfect sence once I extened each side to a point in the middle.


Matt,
Wiill do.
The "box" is really a six sided bird feeder project my grandson is doing for cub scouts. I ran across a picture of one at a craft web site. It looks like it should be simple enough to make one similar to it.



Another example that pizza will save the day every time. It IS the perfect food.





(And doughnuts are the perfect dessert.)



Three cheers for math food.