How it works
For a circular arch, radius equals ((span ÷ 2) squared plus rise squared) divided by twice the rise. Arc length is radius times the central angle in radians, where the angle is twice the arcsine of span divided by twice the radius.
Frequently asked questions
Why is the shortcut span² ÷ 8 × rise wrong?
That shortcut is an approximation for shallow arches and can be about 20% short of the true radius on a tall arch like this one. Use the full formula above.
Does this work for any arch shape?
Only for a circular arc. Pointed, elliptical, and parabolic arches need different geometry.