Description
Return 3(2r-height)²/[4(3r-height)] as distanceFromCenter.
Solid-geometry formulas assume particular shapes and measurement directions. Axial height, slant length, filled-volume centroid, and surface centroid are different quantities even when they describe the same object.
Return 3(2r-height)²/[4(3r-height)] as distanceFromCenter.
When to use this tool
Use Spherical Cap Centroid Axis Offset when you need a local dimension, area, or centroid term for the stated ideal solid.
How to use the tool and how it works
- Enter radius, height. 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 sphere radius and cap height in (0, 2r]. Return 3(2r-height)²/[4(3r-height)] as distanceFromCenter.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. |
| height | Height in the common length unit and direction stated above. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| distanceFromCenter | Centroid offset for a uniform filled spherical cap, not its thin curved surface. | Required. Finite number. |
{
"input": {
"radius": 3,
"height": 3
},
"output": {
"distanceFromCenter": 1.125
}
}Limitations and assumptions
- This is the centroid along the symmetry axis of a uniformly filled solid spherical cap, measured from sphere center toward its apex; it is not the centroid of a thin surface cap or a supplied density distribution.
- 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 solid model for clipping, oblique shapes, or nonuniform material. Confirm radius, height, and centroid conventions before applying an ideal-shape identity.
References
Similar or alternative tools
- Sphere Cap Base Radius Ratio
Compute base radius from height × (2r-height), using alternate scaled forms when needed, then divide by sphere radius.
- Circular Segment Centroid Height Factor
Return 4r sin(halfAngle)³/[3(2 × halfAngle-sin(2 × halfAngle))].