Circle from three points calculator

Enter the coordinates of three points. The tool finds the circle through all of them: its center, radius, the equation in standard and general form, and the diameter, circumference and area.

x₁

y₁

x₂

y₂

x₃

y₃

Center (h, k)(2, 1.5)

Radius (r)2.5

Standard form: (x − 2)² + (y − 1.5)² = 6.25
General form: x² + y² − 4x − 3y + 0 = 0
Diameter: 5
Circumference: 15.70796327
Area: 19.63495408

Runs in your browser: nothing you enter is sent anywhere.

How to use it

Type the x and y of each point.
Read the center and radius, then copy the equation you need.

How it works

With d = 2 × (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)), the center is found from the squared distances of the points to the origin, and the radius is the distance from the center to any point. When d is 0 the points are collinear.

Worked example

Points (0, 0), (4, 0), (0, 3) form a right triangle, so the hypotenuse from (4, 0) to (0, 3) is a diameter. The center is (2, 1.5), the radius is 2.5 and the equation is (x − 2)² + (y − 1.5)² = 6.25.

Tips

Large coordinates close together can lose precision; shift them so one point is the origin.
A radius that comes out huge means the points are nearly in a line.

Frequently asked questions

How is the center found?

The center is where the perpendicular bisectors of the segments between the points meet. It is the circumcenter of the triangle the points form.

Why is there no answer for some points?

If the points are collinear, or two of them coincide, there is no circle through all three.

What are the standard and general forms?

Standard form is (x − h)² + (y − k)² = r². Expanding gives the general form x² + y² + Dx + Ey + F = 0 with D = −2h, E = −2k and F = h² + k² − r².

Does the order of the points matter?

No. Any order of the same three points gives the same circle.

More in Math

All tools in this category: Math ·Updated November 3, 2026