Description
Return 4r sin(halfAngle)³/[3(2 × halfAngle-sin(2 × halfAngle))].
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.
Return 4r sin(halfAngle)³/[3(2 × halfAngle-sin(2 × halfAngle))].
When to use this tool
Use Circular Segment Centroid Height Factor when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter radius, halfAngle. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read distanceFromCenter. Use the output convention below.
Require positive radius and halfAngle in (0, π] and a positive represented denominator. Return 4r sin(halfAngle)³/[3(2 × halfAngle-sin(2 × halfAngle))].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. |
| halfAngle | Half the segment central angle in radians; full angle is twice this value. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| distanceFromCenter | Distance From Center | Required. Finite number. |
{
"input": {
"radius": 3,
"halfAngle": 1.5707963267948966
},
"output": {
"distanceFromCenter": 1.2732395447351628
}
}Limitations and assumptions
- HalfAngle is half the full segment arc angle in radians and the result is centroid distance from center for a uniform filled circular segment, not its arc. Tiny-angle cancellation and finite precision can cause rejection.
- 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 Sector Centroid Radial Factor
Require full sector angle in (0, 2π] radians and return 4 sin(angle/2)/(3 × angle).
- Chord Sagitta Residual
Compute the minor sagitta using its rationalized expression and return measuredSagitta minus expectedSagitta.