THE FEUTEX TOOLKIT

Circle Overlap Lens

Calculate the shared lens area and common chord where two circles partially overlap.

Geometry workspace● Runs in your browser

01 Your input

First radiuslengthSecond radiuslengthCenter separationlength

02 Your result

View or copy raw result data

Result data

Formula

Area = r**2*acos((d**2+r**2-s**2)/(2*d*r))+s**2*acos((d**2+s**2-r**2)/(2*d*s))-0.5*sqrt((-d+r+s)*(d+r-s)*(d-r+s)*(d+r+s)); Chord = sqrt(4*d**2*r**2-(d**2+r**2-s**2)**2)/d

Sources and model references

https://mathworld.wolfram.com/Circle-CircleIntersection.html

Worked example

Inputs

First radius: 5 length
Second radius: 5 length
Center separation: 6 length

Expected results

Area: 22.3647609 length²
Chord: 8 length

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

How to use this tool

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

Try this example

{
  "r": 5,
  "s": 5,
  "d": 6
}

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.