Calculating the Radius of an Arch


Fine Homebuilding's Tips & Techniques

Sometimes it´s useful to know the radius of an arch or head casing long before the shop work takes place.

I have found that the following formula provides precise dimensions and takes advantage of the simple calculators Calculating the Radius of an Archon the market today. Even calculators without a square-root function can handle this one:

Rise2 + (Span/2)2

2 x Rise

For instance, let´s assume that an arched opening leading from a dining room to the great room has 84-inch tall sides, the span is 96 inches and the center of the arch is to be 96 inches above the floor.

The rise is then 12 inches, as shown in the drawing.

When you substitute the numbers and calculate the formula you get:

Rise2 + (Span/2)2

2 x Rise


122 + (96/2)2

2 x 12


144 + 482



144 + 2304







The radius is 102 inches - with no errors resulting from inadvertent stretching of chalklines or other mechanical limitations, such as trying to lay out a curve with a 102-inch radius on a piece of plywood that´s only 96 inches long.

- Charles W. Davis, Watsonville, Calif.

Tips & Techniques provided by Fine Homebuilding.
©2005 The Taunton Press

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