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Circle Center Calculator.

Find the center and radius from opposite endpoints of a diameter.

On-device calculationNo signup
01

Set your values

Results update as you type.

Center x: 1

Center x

0.000000
Center y: 3

Center y

0.000000
Radius: 3.605551

Radius

0.000000

Results update automatically as you type.

Use Cases

Geometry homework help

Quickly verify the center and radius of a circle when given the diameter's endpoints, saving time on manual calculations.

Example: Given points (2,3) and (6,7), the center is (4,5) and radius is about 2.83.

Graphing circles

Determine the circle's equation in standard form by finding the center and radius from two points on a graph.

Example: From endpoints (-1,2) and (5,2), center is (2,2) and radius is 3, so equation is (x-2)^2+(y-2)^2=9.

Frequently Asked Questions

How do I use the Circle Center Calculator?
Enter the x and y coordinates of two opposite endpoints of a diameter (Point 1 and Point 2). The calculator computes the midpoint as the circle's center and half the distance between the points as the radius.
What is the formula used to find the center and radius?
The center is the midpoint: ((x1+x2)/2, (y1+y2)/2). The radius is half the distance between the two points: sqrt((x2-x1)^2 + (y2-y1)^2) / 2.
Can I use this calculator if the points are not exactly opposite?
No, the calculator assumes the two points are opposite endpoints of a diameter. If they are not, the result will not be the circle's center and radius.

Tips & Common Mistakes

Tips

  • Ensure the two points are exactly opposite each other on the circle (diameter endpoints) for accurate results.
  • Double-check your coordinate signs; a missing negative sign can shift the center incorrectly.
  • Use the calculated center and radius to write the circle's equation in standard form: (x - h)^2 + (y - k)^2 = r^2.
  • If you have the circle's equation, you can verify your center and radius by comparing with the standard form.

Common Mistakes to Avoid

  • Entering points that are not opposite endpoints of a diameter, which gives a midpoint that is not the circle's center.
  • Forgetting to divide the distance by 2 when calculating the radius; the radius is half the diameter length.
  • Mixing up the x and y coordinates when entering the points, leading to an incorrect center.

Last updated: August 13, 2026