Construction · masonry
Brick arch calculator.
Enter the span and rise of a segmental arch to get its radius, arc angle, how many bricks fit around the curve, and the cut angle at each joint.
Arch dimensions
Result
Worked example
A 1000 mm span with a 100 mm rise gives R = 1000²/(8×100) + 100/2 = 1250 + 50 = 1300 mm. The arc angle is 2·asin(1000/2600) ≈ 45.24°, and the intrados arc length is 1300 × 0.7896 ≈ 1026.5 mm. With 100 mm bricks and 10 mm joints, floor(1026.5 / 110) = 9 bricks, each joint cut about 5.03° from the next.
Method and limitations
Formulas: R = s²/(8h) + h/2; θ = 2·asin(s / 2R); intrados arc = Rθ; voussoir count = floor(arc / (brick width + joint)); extrados joint = intrados joint × (R + depth) / R; cut angle per joint = θ / count. A semicircular arch is the special case h = s/2, where R = s/2 and θ = 180°. The circle relations are standard geometry, see the Wolfram MathWorld circular segment page. This is geometry only. Arch thrust, abutment restraint, lintel action, and loads need design by a qualified structural engineer and local code. Actual brick sizes and joints vary, so check the count with a dry lay-out.