About this tool
Work with the equation of a circle in three ways: convert center-radius form to general form, convert general form back to center-radius form, or find the unique circle passing through three points. All math is done in your browser.
The standard (center-radius) form (x − h)² + (y − k)² = r² relates to the general form x² + y² + Dx + Ey + F = 0 by D = −2h, E = −2k and F = h² + k² − r². Going the other way (completing the square) gives h = −D/2, k = −E/2 and r = √(h² + k² − F). For three points, the calculator solves the 3×3 linear system for D, E and F using Cramer's rule, then recovers the center and radius.
Every mode also reports the center (h, k), the radius r, the enclosed area πr² and the circumference 2πr. If the coefficients describe no real circle, or the three points are collinear, the input is flagged as invalid.