# Equation of a circle from three points calculator

# Equation of a circle from three points calculator

**To find the equation of a circle passing through three points, follow these steps:**

- Calculate the midpoint of two of the points. Suppose we have three points, A(x1, y1), B(x2, y2), and C(x3, y3), then we can select any two points, say A and B, and calculate their midpoint M((x1+x2)/2, (y1+y2)/2).
- Calculate the slope of the line passing through points A and B. The slope of the line is given by m = (y2 – y1) / (x2 – x1).
- Calculate the slope of the line perpendicular to AB. The slope of the line perpendicular to AB is given by -1/m.
- Calculate the midpoint of the line perpendicular to AB that passes through M. This point is the center of the circle.
- Calculate the radius of the circle. The radius is given by the distance between the center and any of the three points, such as A, B or C.
- Write the equation of the circle in standard form. The equation of the circle is (x – h)^2 + (y – k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

You can use the above steps manually or you can use an online calculator to find the equation of a circle from three points.