Description
Calculate an ideal cone's slant length and slant angle above its base.
Planar orientation and geometric projections depend on the direction of axes and vectors as well as length units. Signed area and height retain side information, while chord sagitta and cone slant angles use specific ideal shapes. Finite-precision formulas and degenerate boundary cases require explicit interpretation.
Calculate an ideal cone's slant length and slant angle above its base.
When to use this tool
Use Cone Base To Slant Angle when checking the stated oriented vector, ideal cone or circle convention.
How to use the tool and how it works
- Enter baseRadius, height. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read angleToBaseRadians, slantLength. Use the output convention below.
Require nonnegative radius/height with at least one positive. Return atan2(height,radius) radians relative to the base plane and hypot(radius,height) slant length.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| baseRadius | Base Radius | Required. Finite number; minimum 0. |
| height | Height | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| angleToBaseRadians | Slant angle above the base plane, in [0,π/2], including accepted degenerate endpoint cases. | Required. Finite number. |
| slantLength | Slant Length | Required. Finite number. |
{
"input": {
"baseRadius": 3,
"height": 4
},
"output": {
"angleToBaseRadians": 0.9272952180016122,
"slantLength": 5
}
}Limitations and assumptions
- Degenerate zero-height or zero-radius cases are accepted; no real cone geometry, material thickness or structural assessment is performed.
- 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 complete geometry and appropriate robust predicates or uncertainty analysis for near-degenerate inputs and physical design conclusions.
References
Similar or alternative tools
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