Description
Return a circular-segment radius from rise and span.
Architectural curves, stairs and roof planes can be described by ideal radii, angles, linear slopes and reference heights. Arc length differs from chord length, and a plan diagonal differs from a sloping member’s length. These local geometry terms do not evaluate structural capacity or building requirements.
Return a circular-segment radius from rise and span.
When to use this tool
Use Arch Segment Radius From Rise Span when checking the stated ideal curve, tread, slope or reference-plane term.
How to use the tool and how it works
- Enter span, rise. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read radius. Use the output convention below.
Return a circular-segment radius from rise and span. Require both > 0; radius = span²/(8*rise)+rise/2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| span | Span | Required. Finite number; strictly above 0. |
| rise | Rise | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| radius | Radius | Required. Finite number. |
{
"input": {
"span": 8,
"rise": 2
},
"output": {
"radius": 5
}
}Limitations and assumptions
- This assumes a circular chord/sagitta geometry; no actual profile fit, arch thickness or structural stability is assessed.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete spatial design, verified dimensions and qualified professional review for structural, accessibility and construction decisions.
References
Similar or alternative tools
- Arch Intrados Extrados Radius Gap
Return nominal and offset-corrected arch-ring thickness.
- Vault Semicircular Rise Span Check
Check a supplied rise against a semicircular span relation.