Construction Calculator - Site Measurement

Arch Calculator

Estimate basic arch curve length from span and rise.

Reviewed: August 31, 2026

Calculate Arch

For the Arch Calculator, enter arch span and arch rise. It returns an approximate half-ellipse curve length from span and rise; it does not create a structural arch profile.

Construction measuring tools arranged beside a residential building project

Formula used

Curve length uses one-half of Ramanujan's ellipse-circumference approximation with semiaxes span รท 2 and rise

Elliptical arch diagram showing the opening span, center rise, spring points, and half-ellipse curve.

Worked arch example

Arch Calculator example: With half-span a = 4.8 ft and rise b = 3.59 ft, the half-ellipse approximation returns about 13.25 ft of curved length for the entered 9.6-ft span.

What the converted result represents

Use the value for preliminary trim or formwork length only after confirming that an ellipse-style profile matches the drawing.

Limits of the geometric model

A circular segment, three-centered arch, pointed arch, catenary, material thickness, springing detail, and fabrication method have different arc lengths.

Questions specific to this calculation

What shape does the arch-length approximation assume?

Enter clear span and rise. The calculator treats half the arch as a half-ellipse approximation and reports the curved length.