Description
Return 2 × radius × sin(π/(2 × sides))² as sagitta.
Polygon formulas combine edge, angle, and area contributions under a stated shape model. A single shoelace term or turning-angle ratio is only part of a full polygon computation and does not independently validate its boundary.
Return 2 × radius × sin(π/(2 × sides))² as sagitta.
When to use this tool
Use Regular Polygon Side Sagitta when you need a polygon dimension, angle, or local accumulation term.
How to use the tool and how it works
- Enter radius, sides. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sagitta. Use the output convention below.
Require positive circumradius and integer sides at least three. Return 2 × radius × sin(π/(2 × sides))² as sagitta.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; strictly above 0. |
| sides | Sides | Required. Safe integer; minimum 3. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sagitta | Sagitta | Required. Finite number. |
{
"input": {
"radius": 2,
"sides": 3
},
"output": {
"sagitta": 0.9999999999999998
}
}Limitations and assumptions
- Sagitta is the radial gap from one regular polygon side midpoint to its circumcircle, not side length or apothem; no actual polygon or geometric tolerance is checked.
- 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
Evaluate the complete ordered boundary for area, winding, and validity. Use a general polygon method when regularity, simplicity, convexity, or uniform shape assumptions do not hold.
References
Similar or alternative tools
- Regular Polygon Apothem Radius Ratio
Require sides 3-1000000 and return cos(π/sides).
- Regular Polygon Central Angle Halfangle Pair
Return 2π/sides for centralRadians and π/sides for halfRadians.