Circle Equation Calculator

Turn a centre point and radius into the standard and expanded equation of a circle.

Circle equation calculator

Centre x (h) Centre y (k)

Radius r

Standard form: —

Expanded form: —

Diameter: — · Circumference: —

Area: —

Standard form is x minus h squared plus y minus k squared equals r squared, with the centre at (h, k).

Enter the x and y coordinates of the centre.
Enter the radius of the circle.
Read the standard equation, the expanded equation, the diameter, the circumference and the area.

Common questions about the free online circle equation calculator.

It is x minus h squared plus y minus k squared equals r squared, where h and k are the centre and r is the radius.

Enter the centre coordinates and the radius, and the standard and expanded equations appear instantly as you type.

Expanding the brackets gives x squared plus y squared plus D x plus E y plus F equals zero, where D equals minus 2h.

Take half of the x and y coefficients with the opposite sign, then the radius is the square root of h squared plus k squared minus F.

Then the equation describes a single point rather than a real circle, so the tool warns that the radius must be positive.

Yes. Any centre works and the tool writes the signs correctly, so a centre of minus 2 becomes y plus 2.

No. The circle equation calculator works entirely in your browser and never sends your numbers anywhere.

Yes. It is completely free to use, with no sign up, no account and no cap on the number of calculations.

Last updated: October 10, 2026