Enter any one measurement of a circle (radius, diameter, circumference or area) and this free circle calculator finds the rest, plus arc length, sector area and chord length for any angle. Switch modes to write the equation of a circle or find the center and radius from x² + y² + Dx + Ey + F = 0.
For x² + y² + Dx + Ey + F = 0 (divide through first if x² has a coefficient).
Circle formulas
Worked example
A circle with radius 5 cm has diameter 10 cm, circumference 2π(5) ≈ 31.42 cm and area π(5²) ≈ 78.54 cm². A 60° arc of it is 31.42 × 60/360 ≈ 5.24 cm long.
From general form to standard form
To turn x² + y² − 4x + 6y − 3 = 0 into standard form, complete the square: (x² − 4x + 4) + (y² + 6y + 9) = 3 + 4 + 9, so (x − 2)² + (y + 3)² = 16. The center is (2, −3) and the radius is 4. If the right side comes out zero or negative, the equation is a single point or has no real circle.
Frequently asked questions
How do I find the area of a circle?
Square the radius and multiply by π: A = πr². For a radius of 5 cm, A = 3.14159 × 25 ≈ 78.54 cm². If you only know the diameter, halve it first.
How do I find the radius from the circumference?
Divide the circumference by 2π: r = C / 2π. A circumference of 31.4 cm gives a radius of about 5 cm.
What is the equation of a circle?
In standard form it is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius. Expanding it gives the general form x² + y² + Dx + Ey + F = 0.
How do I find the center and radius from the general form?
The center is (−D/2, −E/2) and the radius is √(D²/4 + E²/4 − F). Choose the third mode and enter D, E and F to get them instantly with the completed-square working.
What value of π does the calculator use?
It uses JavaScript’s built-in π to about 15 decimal places (3.141592653589793), then rounds answers for display, so results are more precise than using 3.14 or 22/7.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.