Circle Equation Calculator

How it is calculated

For a centre (h, k) and radius r the tool writes the centre-radius form (x − h)² + (y − k)² = r², plus A = π·r² and C = 2·π·r. A positive centre coordinate is written as (x - h) and a negative one as (x + |h|), so the sign is flipped for you; a coordinate of 0 collapses that term to x² or y². Decimal centres and radii are printed with the decimals they need (up to 4, trailing zeros dropped), so a radius of 2.5 gives r² = 6.25, not 6 or 7. Area and circumference always show 4 decimals. The radius must be above zero; 0, a negative radius or an empty box gives no result.

Common mistakes

• Copying the centre signs straight into the equation. A centre at y = −2 gives (y + 2)², not (y − 2)², because the equation subtracts the centre value.
• Entering the diameter instead of the radius. A circle of width 10 has r = 5, so the right side is 25, not 100.
• Reading the right-hand number as the radius. The 25 in the result is r², the radius squared; the radius is 5.
• Entering a radius of 0 expecting a single point. The radius must be above zero, so nothing is shown.
• Entering a general-form equation's coefficients as the centre. For x² + y² − 6x + 4y − 12 = 0 the centre is (3, −2), half of each linear coefficient with the sign flipped, not (−6, 4).