Arch Calculator

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Semicircular: rise = span/2. Segmental: rise < span/2 (flat circular arc). Elliptical: oval curve. Gothic: two arcs meeting at a point.
Horizontal distance from one springer to the other at the spring line.
mm
Vertical distance from the spring line to the highest point (apex) of the arch. For a semicircular arch this equals span / 2.
mm
Thickness of the arch from front to back (e.g. wall thickness or brick length). Used to calculate volume.
mm
Rise is calculated from the span and radius for a semicircular, elliptical, or gothic arch.
mm
RadiusSemicircular
600

Radius of the circular arc (or equivalent radius for elliptical/gothic arches)

Rise600
Arc length1,885
Enclosed area565,487
Central angle180deg
Volume121,579,636
Rise-to-span ratio0.5
Unitmm
Radius600
Arc length1,885
Rise600

Semicircular arch: span 1200 mm, rise 600 mm, radius 600 mm.

  • Rise-to-span ratio is 0.500 (50%). Ratios below 0.1 can create high horizontal thrust - consult a structural engineer.
  • The intrados arc length is 1885.0 mm, which drives the length of formwork or the number of voussoirs.
  • Enclosed area is 565487 mm². Multiply by arch depth to get the masonry volume.

Next stepFor construction, transfer the radius and spring-line measurements to your work surface with a trammel or compass to lay out the formwork.

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