How to Use the Two Circles Intersection Calculator
Enter the center coordinates and radius of two circles and this tool instantly tells you how they relate to each other, then calculates the exact coordinates of any intersection points. It's handy for checking geometry homework by hand, or for verifying circle-collision logic in graphics and game programming.
The calculation starts by finding the distance d between the two centers, then comparing it against the sum of the radii (r1+r2) and the absolute difference of the radii (|r1-r2|). If d is greater than the sum, the circles are separate. If d is smaller than the absolute difference, one circle is fully contained inside the other.
Anywhere in between, the circles meet, and the calculator uses triangle geometry to derive the two exact intersection points. When the distance exactly equals the sum or the difference, the circles touch at exactly one point — externally or internally tangent. This is useful for coordinate geometry assignments, CAD work, and collision detection in game development.
Frequently Asked Questions
The distance between centers must be less than the sum of the radii and greater than the absolute difference of the radii. Outside this range, the circles are either separate or one is fully contained within the other.
If the distance between centers equals the sum of the radii, the circles are externally tangent. If it equals the absolute difference of the radii, they are internally tangent — in both cases there is exactly one intersection point.