How does the Circle Equation work?

Standard form: (x − h)² + (y − k)² = r² Then: Centre is at (h, k) Then: Radius r = √[(x−h)² + (y−k)²] Then: Area = πr², Circumference = 2πr.

Can you give an example of how to use the Circle Equation?

Example: Input Centre (2, 3), r = 5 gives a result of (x − 2)² + (y − 3)² = 25.

Is the Circle Equation free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Circle Equation?

Our Circle Equation uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Circle Equation

Circle Equation Calculator

Center x (h)

Center y (k)

Radius

The standard form of a circle equation is (x − h)² + (y − k)² = r², where (h, k) is the centre and r is the radius. This form makes it easy to identify the centre and radius directly.

Symbol	Name	Unit	Description
h	x-coordinate of center	—	—
k	y-coordinate of center	—	—
r	radius	length	—
x	x-coordinate on circle	—	—
y	y-coordinate on circle	—	—

Radius	Area	Circumference
1	3.14	6.28
5	78.54	31.42
10	314.16	62.83
r	πr²	2πr

References

›Circle equations — Khan Academy

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