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Geometry

Circle Intersection Area Calculator

Find the shared area of two disks from their radii and center separation.

Use consistent dimensionsArea and volume units explained below
Geometry desk
Geometry desk

Match each dimension to the shape and keep units consistent.

See the method

Set the dimensions

Runs on your device

Your measurement

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter first radius, second radius, center separation.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Disjoint circles have zero overlap; containment gives the smaller disk area. Otherwise sum two circular sectors and subtract their triangle areas.

A WORKED EXAMPLE

Using first radius = 3 units, second radius = 3 units, center separation = 3 units, the result is 11.0553273 square units. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Euclidean disks, including containment, tangency and equal coincident disks. Extremely near-tangent cases are sensitive to rounding.

What to keep in mind

Euclidean disks, including containment, tangency and equal coincident disks. Extremely near-tangent cases are sensitive to rounding. Use the indicated units consistently. Ideal shapes are assumed; dimensions must describe the same object. Display rounding does not increase measurement precision.

Common questions

How do I use this circle intersection area calculator?

Find the shared area of two disks from their radii and center separation. Enter first radius in units, second radius in units, center separation in units. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Euclidean disks, including containment, tangency and equal coincident disks. Extremely near-tangent cases are sensitive to rounding.

Methodology maintained by ClarityKit. How these tools are built and checked.