Description
Return atan2(radius,height) for axisAngleRadians and its complementary atan2(height,radius) for normalAngleRadians.
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 atan2(radius,height) for axisAngleRadians and its complementary atan2(height,radius) for normalAngleRadians.
When to use this tool
Use Cone Normal Cross Section Angle Term 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 axisAngleRadians, normalAngleRadians. Use the output convention below.
Require positive radius and height. Return atan2(radius,height) for axisAngleRadians and its complementary atan2(height,radius) for normalAngleRadians.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 |
|---|---|---|
| axisAngleRadians | Axis Angle Radians | Required. Finite number. |
| normalAngleRadians | Normal Angle Radians | Required. Finite number. |
{
"input": {
"radius": 1,
"height": 1
},
"output": {
"axisAngleRadians": 0.7853981633974483,
"normalAngleRadians": 0.7853981633974483
}
}Limitations and assumptions
- This uses a right circular cone; the first is generator-to-axis angle and the second normal-to-axis angle in the meridian plane, without inferring full apex angle or actual solid geometry.
- 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
- Cone Apex Angle Radius Height
Return atan2(radius,height) as halfAngle and twice it as apexAngle.
- Geometry: Cone Generatrix Angle From Radii
Return atan2(absolute radius difference,height) in degrees and the corresponding hypotenuse as slantLength inside result.