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Center of Circle Calculator

Find the center coordinates of a circle from its standard, parametric, or general equation.

(x − A)2 + (y − B)2 = C

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Center of Circle Calculator

Given the equation of a circle, our Center of Circle Calculator instantly extracts its center coordinates — no matter which form the equation is written in. Choose between the standard, parametric, or general form, enter the coefficients, and get the exact center (and radius, where applicable) right away.

What Is the Center of a Circle?

Every circle is defined by two things: its center point and its radius. The center is the fixed point that is equally distant from every point on the circle's edge. Depending on how the circle's equation is written, finding that center can mean reading off two coefficients directly — or doing a small bit of algebra first.

The Three Equation Forms

Standard Form: (x − A)2 + (y − B)2 = C. The center is simply (A, B), and the radius is √C. Be careful of the signs — A and B are subtracted in the equation, so a term like (x + 3)2 means A = −3.
Parametric Form: x = A + r·cos(α), y = B + r·sin(α). Here A and B are the center coordinates directly, while r and α trace out a specific point on the circle's edge.
General Form: x2 + y2 + Dx + Ey + F = 0. The center is (−D/2, −E/2), and the radius is √(D²/4 + E²/4 − F).

Example Calculations

Standard Form: (x − 2)2 + (y + 3)2 = 25

Here A = 2, B = −3, C = 25

✓ Center = (2, −3), Radius = √25 = 5

General Form: x2 + y2 − 4x + 6y − 12 = 0

Here D = −4, E = 6, F = −12

✓ Center = (−(−4)/2, −6/2) = (2, −3)

✓ Radius = √(16/4 + 36/4 + 12) = √25 = 5

Features of Our Center of Circle Calculator

✅ Supports standard, parametric, and general equation forms
✅ Instantly computes center and radius
✅ Clear, step-by-step formulas shown for each form
✅ Free to use, no sign-up required

Who Can Use This Calculator?

Students & Teachers – For geometry and coordinate geometry homework
Engineers & Designers – For CAD, layout, and circular design work
Programmers – For verifying circle equations in graphics or physics code
Puzzle & Exam Solvers – For quickly checking worked-out answers

👉 Try our Center of Circle Calculator to find any circle's center in seconds, no matter which equation form you're working with.