What this calculator does
Arch radius from rise and span works out radius of the circular arc that gives a doorway or window arch its rise and span. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formularadius = rise/2 + span² / (8 × rise), the standard circular-segment (sagitta) formula
The inputs explained
| Field | What to enter |
|---|---|
| Span (arch width) (mm) | A number, measured in mm. Starts at 900. |
| Rise (arch height) (mm) | A number, measured in mm. Starts at 150. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with span (arch width)
Every other input is held at the calculator’s starting values while span (arch width) varies. Select any row to load that scenario into the calculator.