⭕ Equation of a Circle Calculator
Enter a circle’s center coordinates and radius to get its standard-form and general-form equations, plus area and circumference.
What is the equation of a circle?
Every circle can be described algebraically once you know its center point and radius. The most common way to write it is standard form: (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.
How this calculator works
From your center and radius, this calculator computes r² for the standard form equation, and also expands it into general form, x² + y² + Dx + Ey + F = 0, using D = −2h, E = −2k, and F = h² + k² − r². It also reports the circle’s area (πr²) and circumference (2πr) as useful related measurements.
A negative radius isn’t geometrically meaningful, so this calculator automatically uses its absolute value.
This calculator is for general educational and reference purposes.