Center of a Circle Calculator

Welcome to the center of a circle calculator that finds the center of a circle for you. Here, we'll show you how to calculate the center of a circle from the various circle equations. We'll also cover finding the center of a circle without any math!

The center of a circle calculator is easy to use.

1. Select the circle equation for which you have the values.
2. Fill in the known values of the selected equation.
3. You can find the center of the circle at the bottom.

Read on if you want to learn some formulas for the center of a circle!

Circles can be defined with multiple equations. If you have a mathematical formula for your circle, pick the correct one from the headings below. We'll then explain how to calculate the center of the circle from there.

The standard equation of a circle

The standard equation of a circle is:

where $C = r^2$, or the radius squared.

With this equation, we can find the center of the circle at point $(A, B)$. Be careful of the signs!

The parametric equation of a circle

The parametric equation of a circle is defined as:

In this form, we can calculate the center of the circle as $(A,B)$ again.

The general equation of a circle

A less common circle equation is the general equation of a circle:

In the general equation, we can calculate the center of the circle as $\left(-\frac{D}{2}, -\frac{E}{2}\right)$.

If you have a circle drawn on paper, there's no center of a circle formula. Instead, follow these steps:

1. Draw two (or more) chords on the circle.
2. Find these chords' midpoints.
3. From the midpoints, draw lines that are perpendicular to the chords.
4. The point where these lines intersect is the circle's center.
5. Congrats, you can find the center of the circle!

Need to know more about circles? Try some of our other circle calculators, like:

• Equation of a circle calculator;
• Standard equation of a circle calculator;
• General form of the equation of a circle calculator;
• Equation of a circle with diameter endpoints calculator;
• General to standard form of a circle calculator; and
• Standard form to general form of a circle calculator.

The center of this circle is (−9, 6), with a radius of 10. The equation (x+9)² + (y−6)² = 10² is in the standard circle equation form (x−A)² + (y−B)² = C, making A = −9 and B = 6.

The center of this circle is (5, −6), with a radius of 4. The equation (x−5)² + (y+6)² = 4² is in the standard circle equation form (x−A)² + (y−B)² = C, making A = 5 and B = −6.

The center of this circle is (5, −7), with a radius of √81 = 9. The equation (x−5)² + (y+7)² = 81 is in the standard circle equation form (x−A)² + (y−B)² = C, making A = 5 and B = −7.