Circle Equation Calculator

Use three non-collinear points or x² + y² + Dx + Ey + F = 0 to solve the circle center, radius, equation forms, area, and circumference.

Point A

Point B

Point C

Center = —(x − h)² + (y − k)² = r²

—Radius

—Area

—Circumference

—General form

Three-point mode requires non-collinear points. General mode assumes equal x² and y² coefficients with no xy term; otherwise the curve is not this circle form.

Circle Equation Calculator: Forms, Intercepts & Graph

Convert circle equations, inspect center, radius, area, intercepts and point position, and verify geometry with a scaled SVG graph.

Test point X

Test point Y

Graph extent

Practical guide and verification

Standard form exposes the geometry

A circle centered at (h,k) with radius r can be written as (x−h)²+(y−k)²=r². Reading the signs carefully is important because the center coordinate is the opposite sign of the value shown inside each parenthesis.

General form needs completing the square

An equation such as x²+y²+Dx+Ey+F=0 can be converted to center-radius form by completing the square for x and y. The x² and y² coefficients must match for an ordinary circle after normalization.

Common mistake

A negative value for r² after simplification does not represent a real circle in the Cartesian plane. A zero radius is a degenerate point rather than a circle with area.

Use consistent measurements and valid geometric assumptions

Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.