Cone Apex Angle Radius Height Tool

Description

Return atan2(radius,height) as halfAngle and twice it as apexAngle.

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) as halfAngle and twice it as apexAngle.

When to use this tool

Use Cone Apex Angle Radius Height 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 halfAngle, apexAngle. Use the output convention below.

Require nonnegative radius and positive height. Return atan2(radius,height) as halfAngle and twice it as apexAngle.^[1]

Input field	Meaning and units	Accepted input
radius	Radius in the common length unit, with its geometric role defined above.	Required. Finite number; minimum 0.
height	Height in the common length unit and direction stated above.	Required. Finite number; strictly above 0.

Output field	Interpretation	Returned shape
halfAngle	Half Angle	Required. Finite number.
apexAngle	Apex Angle	Required. Finite number.

json

{
  "input": {
    "radius": 3,
    "height": 3
  },
  "output": {
    "halfAngle": 0.7853981633974483,
    "apexAngle": 1.5707963267948966
  }
}

Limitations and assumptions

Both outputs use radians in a right circular cone model; radius zero is accepted as a degenerate limit and no actual cone or useful design range is verified.
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

Calculation and input contract: geometry/cone-apex-angle-radius-height — tool.io

Similar or alternative tools

Geometry: Cone Generatrix Angle From Radii
Return atan2(absolute radius difference,height) in degrees and the corresponding hypotenuse as slantLength inside result.
Cone Normal Cross Section Angle Term
Return atan2(radius,height) for axisAngleRadians and its complementary atan2(height,radius) for normalAngleRadians.