How to use circular arch layout
What this calculation does
A circular arch is determined here by its straight chord width and the rise from that chord to the arc midpoint.
Measure the chord and its central rise, with the rise no greater than half the chord for the supported minor arc.
Enter the measurements
- Straight chord width: Measure the straight distance between arc endpoints.
- Rise from chord to arc: Measure from the chord midpoint to the arc.
Formula and variables
Radius = (chord² ÷ 4 + rise²) ÷ (2 × rise). Center drop = radius − rise. Minor arc length = radius × 2 × asin(chord ÷ (2 × radius)).
Radius = (chord²÷4+rise²)÷(2×rise). Center drop subtracts rise from radius; minor arc length uses the corresponding central angle.
Read the result
A 24 in chord with a 3 in rise has a 25.5 in radius and about 24.988 in of minor arc.
Worked example
Inputs: 24 in chord with 3 in rise
- Radius = (24²÷4+3²)÷(2×3) = (144+9)÷6 = 25.5 in.
- Center drop = 25.5−3 = 22.5 in; arc length ≈ 24.988 in.
Expected result: 25.5 in radius, center 22.5 in below chord, arc about 24.988 in
Frequently asked questions
Does this model an elliptical arch?
No. It assumes a circular minor arc.
Does the arc length include stock allowance?
No. Add fitting, moulding and fixture allowances separately.
Conditions, presets and technical notes
Assumes a circular minor arc, with positive rise no greater than half the chord. Does not calculate a compound, elliptical or pointed arch, molding springback, or stock/fixture allowances.