By Zencalcy Editorial TeamLast reviewed About us
A circular arch is a segment of a circle, and once you know any two of the span, rise, radius and angle, the rest fall out of circle geometry. Builders usually measure the span and rise on site, from which the radius determines every bend and cut.
Arc length, rise, radius and chord of an arch.
radius = (span² ÷ (8 × rise)) + rise ÷ 2 angle = 2 × asin(span ÷ 2R) arc = R × angle (radians)
The rise is measured from the chord to the crown, perpendicular to the span. A rise of half the span is a semicircle — anything less is a segment arch, anything more a horseshoe.
| Symbol | Meaning |
|---|---|
| c | Chord or span of the arch. |
| s | Rise or sagitta of the arch. |
| R | Radius of the parent circle. |
Radius is 87 inches, the arc turns through 87.2°, and the arch curve itself measures 132.4 inches.
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R = (120² ÷ (8 × 24)) + 24 ÷ 2 = 75 + 12 = 87 inches. Every point on the arch sits 87 inches from that center.
Results use standard construction estimating arithmetic: volumes from measured area and depth, unit weights from published material densities, and code-referenced spans or clearances where the page names a code. Quantities are rounded up to whole saleable units and include the stated waste allowance. These tools are planning aids, not structural design, and do not replace a licensed engineer, a local code check, or a contractor's site measurement.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026