Center of Circle Calculator

Formula

To calculate the center of a circle (h, k):

\[ (h, k) = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) \]

Where:

\( (h, k) \) is the center of the circle (coordinates)
\( (x1, y1) \) and \( (x2, y2) \) are the coordinates of two points on the circle

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.

Example Calculation

Let's assume the following values:

X-coordinate of Point 1 \( x1 \) = 2
Y-coordinate of Point 1 \( y1 \) = 3
X-coordinate of Point 2 \( x2 \) = 8
Y-coordinate of Point 2 \( y2 \) = 7

Step 1: Use the center of circle calculation formula:

\[ (h, k) = \left( \frac{2 + 8}{2}, \frac{3 + 7}{2} \right) = (5, 5) \]

The center of the circle is (5, 5).