🏰 Arch Calculator
Calculate the radius and arc length of a circular arch based on its span and rise.
1
in
2
in
What this calculator does
This tool calculates the radius of a circular arch (a segmental or true arch shape used in doorways, windows, and decorative openings) from its span (width) and rise (height at the center).
The formula
Radius = (half-span² + rise²) ÷ (2 × rise). This comes from the geometry of a circular segment. The arc length and included angle are then found using the arcsine of half-span ÷ radius.
This assumes a true circular arch. Elliptical, Gothic, and other non-circular arch shapes use different geometry and will not match this formula exactly.
Last reviewed August 2026