How this calculation works
At a centre distance equal to the sum of the radii, the circles touch at a point and their intersection area is zero.
Partial overlap = sum of two circular sectors minus two trianglesA worked example
A radius-1 disc with its centre 0.5 from a radius-2 disc is fully contained. The overlap is π.
Good to know
Use the same length unit for the radii and centre distance.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the intersection area of two discs, including disjoint and contained cases.
The primary result is labeled “Overlap area”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Use the same length unit for the radii and centre distance.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
A radius-1 disc with its centre 0.5 from a radius-2 disc is fully contained. The overlap is π.
Which rule does this calculator apply?
Partial overlap = sum of two circular sectors minus two triangles