How To Calculate Segmented Radius For Building Arches - Master Carpenter Secrets Revealed 

There is a mistake in example #2 - where 468 should be 636.025 and thank you Apophis.

Beautiful

Great information. Knew it was out there somewhere. Just hadn't stumbled across it until today. Thx!

Great help, thanks.

Formula is (h^2 + w^2)/(2h), where h is the desired height of the arch, w is half the width of the opening. Algebra is much cleaner. Thanks for sharing.

Thank you. Big long arch exactly 14 inchesx 14ft to work on tomorrow. It's a casing arch over a window using maple hardwood

Thank you

very useful video sir ihave ever seen at site frequently face this problem that how can we find arch radius without auto cad at site and you solved my problem brother thanks alot for making this informative video

I think it should be " 12 divided into 468" or you could say 468 divided by 12

Great video Greg, Here is another way of doing the calculations that does not involve squaring two numbers or needing to write down numbers to then use them later in the calculation. Here it is R = Dw² ÷ (8×Jp) + Jp÷2 where Dw is the door width; Jp is the jamb intersect point (or height of the arch); and of course R is the radius you’re looking to calculate. In your first example Dw=36”; Jp=12” therefore R= 19.5”. In the calculator just type 36 x² ÷ 8 ÷ 12 = + 12 ÷ 2 = {x² is a function key, it appears on most calculator apps by turning your cell phone horizontal} try it love ur videos -Eddie

In example 2 you calculated 36 + 600.25 = 636.25 which is correct then under 6 times 2 = 12 you annotated 12 / 468 = 53.02 (468 from example 1). I now know the calculation should be 636.25 / 12 = 53.02. Just learning this stuff and it threw me for a loop.

I noticed in each example, you used different height. What determines the height? Is it builder preference or is it based on opening?

in the third example, how did you arrive at 14" ?

I have a question. What not just use basic geometric principles without numbers, i.e. without calculations? I mean, what is the benefit of doing it this way? I though a master carpenter, or at least a master in the classical approach I guess, would use nothing more than a compass and straight edge (and perhaps a ruler only for determining height and width of the wall) if he were drawing it on a plan. Even easier on a computer, just add the circle and let the computer spit out the final measurements. Recently I’ve been doing no-math geometry and could easily create those arcs with no calculations. If the height and width are given, I could do a scaled down version (just reducing ratios like a triangle [architecture/engineering] ruler does). The only number I might need is the amount to subtract from the center to achieve the desired result (e.g. -3” from center). And I am doing this with pencil and paper. There might be a learning curve doing it on a computer, but once the principles and methods are known, it would be even quicker and more accurate. Even taking your time on paper there is a slight imperfection, even only microscopic. But nothing is truly perfect except on paper anyhow, so to speak.

Height times 2 is really; 2 times the height.

Also, isn’t the radius simply half of the opening (assuming squared opening like any regular door/window would be)? Just measure the opening edges and divide in half. No simplification of fancy formulas needed. It doesn’t get any simpler.

If you could correct your formula would make a lot more sense. Your number divisions are back to front. 24 divided by 468 certainly isn’t 19.5, but 468 divided by 24 is.😁