A few years ago I posted an article about The Best Way To Brace A Wooden Door Or Gate. Some folks wanted to know if there was a way to use trigonometry to calculate things like the mitre angle for the brace, so it could be just cut on a mitre saw without a whole bunch of test fitting and shaving. Well, yes, there is.

If we let:

**bW** be the brace Width
**rL** be the rail Length
**dBR** be the distance Between Rails

then:

**bL** ( **brace Length** ) = sqrt( rL^2 + dBR^2 – bW^2 )
**mA** (**mitre Angle** (in degrees)) = 180/pi * ( pi/2 – arctan( dBR / rL ) – arcsin( bW / sqrt( rL^2 + dBR^2 ) ) )

Note that if you are using a calculator to crunch mA then you need to switch from DEGrees mode to RADians mode. Arcsin is undefined outside of +/-1 so you can’t use degrees within that function — you need to use radians and then convert the answer back to degrees at the end (which is what the 180/pi multiplier does). The answer produced by the equation is in degrees.

For those interested in where the above came from, here is what I originally worked out on the back of an envelope, tidied up so that (hopefully) it can be read and understood by others:

Let me know if you spot any mistakes.

Cheerio!

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Thank you very much. I have worked through the calculations and I can’t find an error. I have also used trigonometry to calculate the length of the mitred end of the brace as bw/sin (bA) in your notation. That length is not necessary, but it may come in handy for someone who wants to check their measurements.

Thanks Steve.