Circle intersection calculator
Find where two circles meet and measure their overlap. Enter both centers and radii, then download the diagram and intersection coordinates.
Use the same measurement unit for every coordinate and radius. Coordinates must be finite with magnitudes up to 1,000,000,000. A radius may be zero or between 0.000000001 and 1,000,000,000. Positive Y points up. Results use floating-point arithmetic, not exact symbolic geometry. Cases within the displayed numerical tolerance are treated as tangent; overlap area is measured in the square of your coordinate unit. Coincident circles have infinitely many intersections, represented explicitly rather than as a fabricated point list. Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.
Your result
How to use Circle intersection calculator
- Enter the X and Y coordinates of each center and both radii.
- Read the relationship, intersection count and overlap area. The diagram uses one scale for both circles.
- Download the intersection points as CSV, the full calculation as JSON or the diagram as SVG.
Useful next steps
Two circles, one coordinate system
Use the same unit for all six inputs. For two unit circles centered at (0, 0) and (1, 0), the intersections are (0.5, 0.8660254…) and (0.5, -0.8660254…). The overlap area is approximately 1.2283697 square units.
Handle every relationship
Separated circles have no shared area. Contained circles have the area of the smaller circle in common. Tangent circles meet at one point. Identical nonzero circles share infinitely many points. A zero-radius circle is treated as one point.
Keep precision in the download
The visible result uses localized display numbers. CSV and JSON preserve the calculated numeric values. The numerical tolerance is based on floating-point precision and the scale of the circles; this is not exact symbolic geometry.