Mitering a circle

[Dave225]

Is there a formula or chart for detemining the length of a piece of wood that’s used as a segment in a circle?

Example: If I cut eight pieces of wood equal lengths and miter the ends at 22.5° and glue them together, I will end up with a semicircle. The question is, to make a semicircle that’s 30 inches in diameter, what is the length that I need to cut each segment?

I would assume that there would be an existing chart or formula somewhere to figure this out…

Or, who’s good at geometry?

[deecee]

today, but I am curious how you ended up with your compressor motor repairs. ????

Luck, Kizmet

[tom]

Do a google search on “chord length”.

I don’t have the formula handy but it would be there.

[Johnny]

I’ve never had a geometry class, but am pretty good at figuring these things out. I hope this does not need to exact as I will be rounding to the hundreths and a true circle is round whereas what you are talking about is made from straight pieces:

We know that: Pi R2 = circumference

We know: R = 1/2 Diameter,

So we can say Pi D = circumference

So circumference = 3.1416 x 30 = 94.25

We know the circumference of a semi-circle is half of a circle, so the outside of this semi-circle is 47.125.

You want to use 8 straight pieces to miter together, so 47.125/8 = 5.890625, or 5 57/64.

For ease, round to 5 56/64, or 5 7/8, and you will have a semi-circle with an approximate 29.92 inch diameter.

I’m sure I do not need to say this, but if you want the id to be approx 30, the 5 7/8 needs to be on the mitered length (short side), if you want an approx 30 in od, the unmitered length (long side), needs to be 5 7/8.

[homebild]

If the diameter is 30″, the length of each cut will be 15″.

The radius (which happens to be the exact length of each side) is 1/2 the diameter.

[Author]

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