Circle Calculator
Variable Key
Given radius r
Calculate diameter, circumference, and area from the radius.
Given diameter d
Calculate radius, circumference, and area from the diameter.
Given circumference C
Calculate radius, diameter, and area from the circumference.
Given area A
Calculate radius, diameter, and circumference from the area.
A circle is the set of all points in a plane that are exactly the same distance (the radius) from a central point. All four measurements — radius, diameter, circumference, and area — can be calculated from just one known value using the mathematical constant π (pi ≈ 3.14159).
Tip: The circumference of the Earth at the equator is about 40,075 km. Its radius is about 6,371 km. Check: 2π × 6,371 ≈ 40,030 km — close!
- 1Radius (r): the distance from the centre to any point on the circle
- 2Diameter (d): twice the radius — d = 2r
- 3Circumference (C): the perimeter of the circle — C = 2πr = πd
- 4Area (A): the space enclosed — A = πr²
Unit circle
A circle with radius = 1 is the unit circle. It defines the trigonometric functions sin and cos for all angles.
Pi (π) exactly
π is irrational — its decimal expansion never repeats or terminates. Computed to over 100 trillion digits as of 2022.
| Radius r | Diameter d | Circumference C | Area A |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.5664 | 12.5664 |
| 5 | 10 | 31.4159 | 78.5398 |
| 7 | 14 | 43.9823 | 153.9380 |
| 10 | 20 | 62.8318 | 314.1593 |
| 12 | 24 | 75.3982 | 452.3893 |
| 15 | 30 | 94.2478 | 706.8583 |
Fun Fact
A circle has the largest area of any shape with the same perimeter — this is called the isoperimetric inequality. Nature uses this: soap bubbles and planets form spheres for the same reason.
References