Center Of Circle Calculator – 3 Points or Equation

Find a circle’s center and radius from three points, diameter endpoints, or general-equation coefficients, with collinearity and point-fit verification.

Center Of Circle Formula

If (x1, y1) and (x2, y2) are the endpoints of a diameter of the circle, then the center is the midpoint of those two points.

(h, k) = ((x₁ + x₂) / (2), (y₁ + y₂) / (2))

Variables:

(h, k) is the center of the circle (coordinates)
(x1, y1) and (x2, y2) are the coordinates of the two diameter endpoints

To calculate the center of a circle from diameter endpoints, add the x-coordinates of the two endpoints and divide by 2 to get the x-coordinate of the center (h). Similarly, add the y-coordinates of the two endpoints and divide by 2 to get the y-coordinate of the center (k).

What is a Center Of Circle?

A center of a circle is a specific point inside the circle from which all points on the circumference (boundary) of the circle are equidistant. In other words, if you draw a line from the center to any point on the circle's edge, that line, known as the radius, will always be the same length, no matter which point on the circle you choose.

How to Calculate Center Of Circle?

The following steps outline how to calculate the Center of Circle using the given formula:

First, determine the coordinates of the two endpoints of a diameter, (x1, y1) and (x2, y2).
Next, substitute the values of (x1, y1) and (x2, y2) into the formula: (h, k) = ((x1 + x2) / 2, (y1 + y2) / 2).
Finally, calculate the center of the circle, (h, k), using the formula.
After inserting the values and calculating the result, check your answer by confirming both points are the same distance from the computed center (i.e., they give the same radius).

Example Problem:

Use the following variables as an example problem to test your knowledge (assume the two points are diameter endpoints):

(x1, y1) = (3, 5)

(x2, y2) = (7, 9)

Center: (h, k) = ((3 + 7) / 2, (5 + 9) / 2) = (5, 7)