What this tool does
Computes the radius, central angle, and arc length of a circular arch from its span and rise — the base geometry for formwork or opening design.
How to use it
- Enter the arch span in metres.
- Enter the rise in metres; it must not exceed half the span.
- Run it for radius, central angle, and arc length.
Worked example
A 4 m span with a 1 m rise gives a radius of 2.5 m, a central angle of about 106.26 degrees, and an arc length of about 4.64 m.
Calculation method
Circular arc radius
span^2/(8*rise)+rise/2Central angle
4*atan(2*rise/span)*180/piArc length
(span^2/(8*rise)+rise/2)*4*atan(2*rise/span)Frequently asked questions
- What if the rise equals half the span?
- You get a semicircular arch: the radius is half the span and the central angle is 180 degrees. A greater rise cannot be described as a circular arch and falls outside the range.
- What is arc length used for?
- Sizing material that follows the curve — formwork banding, trim, and moulding. For an arch with thickness, compute the inner and outer radii separately.
What this tool does not cover
Circular arch geometry only. Structural strength, load paths, reinforcement, and elliptical or parabolic arches are out of scope.