Construction

Arch Calculator

Find an arch's radius and arc length from span and rise.

Span (width)

Rise (height)

Calculated Output

Radius 0.625

Arc length 1.159

Formula: radius = (span² + 4·rise²) ÷ (8·rise)

Step-by-Step Breakdown

1. Values used:

2. Span (width) = 1

3. Rise (height) = 1

5. Radius = 0.625

6. Arc length = 1.159

Did this calculator solve your problem today?

The math behind it

radius = (span² + 4·rise²) ÷ (8·rise); arc length = radius × central angle (radians).

8 ft span, 3 ft rise → radius 4.17 ft, arc ~9.8 ft.

Door arch?

Use this for curved doorways, window arches and niche surrounds.