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Calculation Machine

Circle Equation Calculator

Centre, radius, standard and general form of any circle.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Standard form
(x − 3)² + (y + 2)² = 25
General form
x² + y² − 6x + 4y − 12 = 0
Circumference
31.4159
Area
78.5398
Diameter
10
Bounding box
x from -2 to 8, y from -7 to 3

Quick answer

A circle with centre (h, k) and radius r has the equation (x − h)² + (y − k)² = r², which expands to the general form x² + y² + Dx + Ey + F = 0.

The formula

(x − h)² + (y − k)² = r²

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Centre x (h)3
  • Centre y (k)-2
  • Radius r5

Result

  • Standard form(x − 3)² + (y + 2)² = 25
  • General formx² + y² − 6x + 4y − 12 = 0
  • Circumference31.4159
  • Area78.5398
  • Diameter10
  • Bounding boxx from -2 to 8, y from -7 to 3

How to use the Circle Equation Calculator

  1. 1Enter the centre coordinates.
  2. 2Enter the radius.
  3. 3Copy the standard or general form, whichever your class or CAD tool expects.

Frequently asked questions

How do I go from general form back to standard?

Complete the square on the x and y terms; the centre is (−D/2, −E/2) and r² = h² + k² − F.

What if the radius comes out imaginary?

Then the general-form equation has no real circle — it describes an empty set or a single point.

About this calculator