Construction / CALCULATOR

Circular Arch from Span and Rise

Circular Arch from Span and Rise: explore an explicit model with input checks, a formula and a worked example.

Runs on your deviceUpdates as you typeFormula & example ↓
01

Your inputs

Adjust the values to explore a different result.

m
Enter span in m.
m
Enter rise in m.

Formula

R=span²/(8 rise)+rise/2; θ=4 atan(2 rise/span); arc=Rθ.
  • Use the units shown beside each field.
  • Results update automatically whenever you change an input.
  • Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
  • Circular minor arch only, not an ellipse or catenary. Quantity estimate only. Confirm actual dimensions, openings, cutting patterns and supplier specifications. No structural design or code-compliance assessment.

Example Calculation

Example inputs
  • Span: 4 m
  • Rise: 1 m

Span 4 m and rise 1 m give radius 2.5 m and arc length about 4.6365 m.

Frequently asked questions

How do I use this calculator?

Enter span, rise. The result updates automatically. Use Reset to restore the example values.

What method does it use?

R=span²/(8 rise)+rise/2; θ=4 atan(2 rise/span); arc=Rθ.. Circular minor arch only, not an ellipse or catenary. Quantity estimate only. Confirm actual dimensions, openings, cutting patterns and supplier specifications. No structural design or code-compliance assessment.

Why might a rounded result differ?

The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.

Are my inputs saved online?

No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.

Check the assumptions and units before using this result. Read about calculation methods.