Convert between centre–radius and general circle equations, with area, circumference and diameter.
Circle equation
How to use this tool
Choose centre–radius or general form.
Enter the centre and radius, or D, E and F.
Read both equation forms plus centre and radius.
Read area and circumference.
Formula & worked example
Centre (3, −4) with radius 5 gives (x − 3)² + (y + 4)² = 25, equivalently x² + y² − 6x + 8y = 0, area 78.54 and circumference 31.42.
Limitations — read this before you rely on it
Real circles only: general forms with a non-positive radius-squared term are reported as errors, not as degenerate point circles.
Frequently asked questions
(x − h)² + (y − k)² = r², where (h, k) is the centre and r is the radius. It reads the centre and radius directly off the equation.
Complete the square: centre (−D/2, −E/2) and radius √((D² + E²)/4 − F). If that radicand is zero you get a point, and if negative, no real circle.
Because (x − h) with h = −4 becomes (x + 4). Watch the sign when reading centres off factored form.
Yes. If they share another coefficient, divide the whole equation by it first.
Area = πr² and circumference = 2πr, using the radius found from either form.