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THE FEUTEX TOOLKIT

Cone Solid Angle and Sphere Fraction

Calculate a cone aperture’s solid angle and the fraction of a sphere it covers.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
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FormulaSolid Angle = 2*PI*(1-cos(theta*PI/180)); Sphere Fraction = (1-cos(theta*PI/180))/2
Sources and model references

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "theta": 60
}

Accuracy and scope

A cone aperture, not the planar sector angle; half-angle is measured from its axis. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.