Circle Calculator
Enter any one of radius, diameter, circumference, or area — get the other three instantly.
From this, r = 5, d = 10, C ≈ 31.4159, A ≈ 78.5398.
Give any one circle measurement and the rest follow. With radius r = 5, the diameter is d = 2r = 10, the circumference is C = 2πr ≈ 31.42, and the area is A = πr² ≈ 78.54. Every result comes from the same radius using π.
How a circle is measured
A circle is fixed by a single number — its radius r, the distance from the centre to the edge. Once you know r, the diameter, circumference, and area are all direct consequences. This tool works backwards too: give it any one of the four and it recovers the radius first, then computes the rest.
circumference is proportional to r; area grows with r²
Worked example
Start from a radius of r = 5 and find all four quantities:
- 1 Note the radius. r = 5 is the distance from the centre to the edge.
- 2 Double it for the diameter. d = 2r = 2 × 5 = 10.
- 3 Multiply by 2π for the circumference. C = 2πr = 2 × π × 5 ≈ 31.42.
- 4 Square the radius and multiply by π for the area. A = πr² = π × 5² = π × 25 ≈ 78.54.
The four quantities from the radius r
Each circle measurement is a direct function of the radius.
| Quantity | Symbol | Formula from r | r = 5 |
|---|---|---|---|
| Radius | r | r | 5 |
| Diameter | d | d = 2r | 10 |
| Circumference | C | C = 2πr | ≈ 31.42 |
| Area | A | A = πr² | ≈ 78.54 |
π, radius, and diameter
π (pi) is the ratio of a circle’s circumference to its diameter, roughly 3.14159. It is irrational, so it never terminates — this calculator carries full double precision and rounds only for display.
Radius vs diameter: the diameter is a full chord through the centre, exactly twice the radius (d = 2r). Mixing the two is the most common circle mistake — using the diameter where a formula wants the radius doubles C and quadruples A.