Circle
Find the area and circumference of a circle from the radius, diameter, circumference or area, and the area of an annulus. Exact answer in terms of π.
The circle calculator finds the area and the circumference of a circle from the radius, the diameter, the circumference or the area, and also the area of an annulus (ring) from two radii. When the radius is a number, the answer is shown both exactly — in terms of π (for example, 25π) — and approximately.
Main formulas
| Value | Formula |
|---|---|
| Diameter | d = 2r |
| Circumference | C = 2πr = πd |
| Area | S = πr² = πd²/4 |
| Radius from the circumference | r = C / (2π) |
| Radius from the area | r = √(S/π) |
| Area of an annulus | S = π(R² − r²) |
The number π ≈ 3.14159 is the ratio of the circumference of any circle to its diameter.
Example 1. Radius 5 cm.
C = 2π · 5 = 10π ≈ 31.42 cm, S = π · 5² = 25π ≈ 78.54 cm².
Example 2. Circumference 31.4 cm.
r = 31.4 / (2π) ≈ 5 cm, S ≈ 78.5 cm².
Example 3. An annulus with radii 5 cm and 3 cm.
S = π(25 − 9) = 16π ≈ 50.27 cm², the width of the ring is 2 cm.
Circle and disk
Strictly speaking, a circle is the curve whose points are at distance r from the center — it has a length (circumference) but no area. The region inside it is a disk, and "the area of a circle" means the area of that disk.
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