Measure the height and width of the arch. The height should be measured up to the point where the arch starts curving. The difference between this number and the height at the center of the arch is called the rise. For example, if the sides are 72 inches tall, and the center of the arch is 84 inches tall, the rise would be 12 inches.
Use the formula Rise^2 + (Span/2)^2 / 2 x Rise to find the radius of the arch. Plug in your numbers, and use the order of operations PEMDAS (parentheses, exponents, multiplications, addition, subtraction) to solve the equation. In the example above, we had a rise of 12 inches. Let's say that the width (or span) is 60 inches. Therefore, the equation becomes 12^2 + (60/2)^2 / 2x12.
Calculate the parentheses first. 60/2 = 30, so the equation becomes 12^2 + (30)^2 / 2 x 12.
Do the exponents next. 12^2 = 144, and 30^2 = 900. The equation should now look like this: 144 + 900 / 12 x 2.
Multiplication is next. 12 x 2 = 24, so we have 144 + 900 / 24.
Add together the numbers on the top of the fraction. 144 + 900 = 1044. 1044/24 can be reduced to 43.5. The radius of the arch is 43.5 inches.