Description
Return atan2(absolute radius difference,height) in degrees and the corresponding hypotenuse as slantLength inside result.
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(absolute radius difference,height) in degrees and the corresponding hypotenuse as slantLength inside result.
When to use this tool
Use Geometry: Cone Generatrix Angle From Radii 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 lowerRadius, upperRadius, axialHeight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require nonnegative lower and upper radii and positive axialHeight. Return atan2(absolute radius difference,height) in degrees and the corresponding hypotenuse as slantLength inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lowerRadius | Lower Radius | Required. Finite number. |
| upperRadius | Upper Radius | Required. Finite number. |
| axialHeight | Axial Height | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated members; expand to inspect the fields below. | Required. Object. |
| result.generatrixAngleDegrees | Generatrix Angle Degrees | Calculated result member: number. |
| result.slantLength | Slant Length | Calculated result member: number. |
{
"input": {
"lowerRadius": 3,
"upperRadius": 0,
"axialHeight": 4
},
"output": {
"result": {
"generatrixAngleDegrees": 36.86989764584402,
"slantLength": 5
}
}
}Limitations and assumptions
- The angle is generator-to-axis for a coaxial right conical frustum; equal radii give a cylinder limit and no oblique geometry, dimensions, or structural performance are validated.
- Outputs are nested inside result. 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.
- Cone Normal Cross Section Angle Term
Return atan2(radius,height) for axisAngleRadians and its complementary atan2(height,radius) for normalAngleRadians.