Octagon Calculator

[kthoennes]

I'm working on an octagon base for a fire table on the patio outside and needed to calculate some dimensions and angles.  I did a search on this site first (of course) for a good octagon calculator and found some search results, but the links didn't work anymore or they seemed more written for a geometry class instead of a woodworking application.  Found this one on a Google search, pretty handy if anybody needs an octagon calculator.  Nice of somebody named Joe Barta to post it.  I sent him a thank you email.    

http://www.pagetutor.com/octagon_layout/

(Now I have to make sure a propane tank will fit inside my octagon...   With vent ports of course so I don't blow the deck off the house.)

[Edwin Hackleman]

Now all you need to do is make a jig that accurately cuts large or small octagons using the table saw. Doing it with a typical miter gauge and the fence alone is virtually impossible. This alone is worth a thread here.

[Phil S.]

You can construct an octagon with a compass or trammel points.  Start with a square the width of the octagon you want.  Take half the diagonal distance between opposite corners.  Swing an arc of that radius from each corner to both adjacent sides. Connect the points to form the octagon.  Picture is worth all of these words-

http://chestofbooks.com/crafts/metal/Met...ctagon.jpg

To fit a propane tank, the square you start with would be the diameter of the tank plus the twice thickness of the material you're using for the sides plus a little more for insurance.  The angle between all the sides of a regular octagon is 135°.

[JGrout]

360/8=45

45/2= 22.5

that is the saw bevel for the rips 

build your octagon from the inside out and the propane bottle will fit

HTH

[MstrCarpenter]

I'm not usually looking for a website to basic math for me, all I want is the equation in it's most simple form. If I also learn why; I have a much better chance of remembering it. Here's what I came up with (without any help from the internet) when I actually needed to know.

I remember that both the sine and cosine of *45 is .707. (I use this frequently on the jobsite to square up foundations when a 3,4,5, triangle doesn't fit well.)

If we look at just the top portion of an octagon, we see a rectangle and two *45 triangles. We know the top of the rectangle is the same size (let's call it 1) as the hypotenuse of the two triangles. If the hypotenuse is 1, then the legs are .707. So let's add them up. .707 + 1 + .707 = 2.414. That's the magic number I was looking for; 2.414!!!

Now for some practical applications:
I have a propane tank that's 18.5" in diameter that has to fit inside an octagon; how wide do the sides have to be?
18/2.414=7.4565, or (.4565x32=14.688/32) 7-7/16+". (Remember that's the inside dimension.)

I have some 1x8 cherry to make an Octagon. Will my wife's ugly 16" flower pot fit inside? Let's find out before we cut it all up. The cherry dresses out at 3/4"x7.25", so 7.25 x 2.414=17.5015, deduct 1.5 for the thickness of the two sides and you'll discover that you'll just scratch the finish as you press it in!

To help you all remember, add it up in your head .707+.707=1.414 (that's the two triangles), now add 1 for the top side; 2.414 Again, it's 2.414, and now you know why. I Know this post may seem stupid and redundant, but hopefully you'll remember 2.414

[AHill]

I'm not usually looking for a website to basic math for me, all I want is the equation in it's most simple form. If I also learn why; I have a much better chance of remembering it. Here's what I came up with (without any help from the internet) when I actually needed to know.

I remember that both the sine and cosine of *45 is .707. (I use this frequently on the jobsite to square up foundations when a 3,4,5, triangle doesn't fit well.)

If we look at just the top portion of an octagon, we see a rectangle and two *45 triangles. We know the top of the rectangle is the same size (let's call it 1) as the hypotenuse of the two triangles. If the hypotenuse is 1, then the legs are .707. So let's add them up. .707 + 1 + .707 = 2.414. That's the magic number I was looking for; 2.414!!!

Now for some practical applications:
I have a propane tank that's 18.5" in diameter that has to fit inside an octagon; how wide do the sides have to be?
18/2.414=7.4565, or (.4565x32=14.688/32) 7-7/16+". (Remember that's the inside dimension.)

I have some 1x8 cherry to make an Octagon. Will my wife's ugly 16" flower pot fit inside? Let's find out before we cut it all up. The cherry dresses out at 3/4"x7.25", so 7.25 x 2.414=17.5015, deduct 1.5 for the thickness of the two sides and you'll discover that you'll just scratch the finish as you press it in!

To help you all remember, add it up in your head .707+.707=1.414 (that's the two triangles), now add 1 for the top side; 2.414 Again, it's 2.414, and now you know why. I Know this post may seem stupid and redundant, but hopefully you'll remember 2.414

 
You were doing good until you did the math - it's 18.5 / 2.414 = 7.66.

[Edwin Hackleman]

So, are small and large octagons easy to cut with only a table saw fence and miter gauge that you can buy at HD? Hmmm... First two cuts might be easy, starting with a square, but after that...

The jig's up.

[MstrCarpenter]

 
You were doing good until you did the math - it's 18.5 / 2.414 = 7.66.

I just measured my propane tank; it's only 12" in diameter. We're still good! But more important is that you remembered 2.414