Math

Equation of a Circle Calculator

Get circle properties from centre (h, k) and radius r.

Calculated Output

Area 78.54

Circumference 31.416

General-form constant -12

Formula: (x − h)² + (y − k)² = r²

Step-by-Step Breakdown

1. Values used:

2. Centre x (h) = 2

3. Centre y (k) = -3

4. Radius r = 5

6. Area = 78.54

7. Circumference = 31.416

8. General-form constant = -12

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The math behind it

Expanding gives the general form x² + y² − 2hx − 2ky + (h² + k² − r²) = 0; the constant term is h² + k² − r².

Centre (2, −3), r = 5 → (x − 2)² + (y + 3)² = 25.

How do I find the radius from general form?

Complete the square in x and y to recover (h, k) and r.