Description
Require full sector angle in (0, 2π] radians and return 4 sin(angle/2)/(3 × angle).
Circle calculations distinguish radius, diameter, chord, sagitta, tangent, and oriented offsets. Branch choices determine signs and which arc or segment is meant; a scalar identity does not always establish an actual geometric construction.
Require full sector angle in (0, 2π] radians and return 4 sin(angle/2)/(3 × angle).
When to use this tool
Use Circular Sector Centroid Radial Factor when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter angleRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read factor. Use the output convention below.
Require full sector angle in (0, 2π] radians and return 4 sin(angle/2)/(3 × angle).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| angleRadians | Full central angle of a uniformly filled sector, in radians. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| factor | Factor | Required. Finite number. |
{
"input": {
"angleRadians": 3.141592653589793
},
"output": {
"factor": 0.4244131815783876
}
}Limitations and assumptions
- The factor multiplies radius to obtain the uniform filled sector's centroid distance from center; it is not an arc centroid and no actual sector or density distribution is inspected.
- 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
Construct the circles, chord, or segment in coordinates when existence or orientation matters. Use the complete geometry and an appropriate tolerance for intersection or tangency decisions.
References
Similar or alternative tools
- Circular Segment Centroid Height Factor
Return 4r sin(halfAngle)³/[3(2 × halfAngle-sin(2 × halfAngle))].
- Circular Annulus Area Bisecting Radius
Return hypot(inner,outer)/sqrt(2).