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THE FEUTEX TOOLKIT

Spherical Triangle Excess and Area

Calculate spherical excess and surface area from three angles on a chosen sphere.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
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FormulaExcess = (a+b+c-180)*PI/180; Area = r**2*(a+b+c-180)*PI/180
Sources and model references

Worked example

Inputs

Angle A
90 degrees
Angle B
90 degrees
Angle C
90 degrees
Sphere radius
2 length

Expected results

Excess
1.570796327 rad
Area
6.283185307 length²

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

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

{
  "a": 90,
  "b": 90,
  "c": 90,
  "r": 2
}

Accuracy and scope

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.