Circle Calculator

How This Calculator Works

A circle’s radius, diameter, circumference, and area are all mathematically related — knowing any one of them lets you find the other three. Pick which one you already know, enter its value, and this calculator solves for the rest instantly.

The Formulas

$$d = 2r \qquad C = 2\pi r = \pi d \qquad A = \pi r^{2}$$

where $r$ is the radius, $d$ is the diameter, $C$ is the circumference, and $A$ is the area. These four formulas have no single “input” variable — each one can just as easily solve for radius as start from it — so they’re left uncolored here rather than assigning one variable a fixed color it wouldn’t consistently play across every direction.

Working backwards from diameter, circumference, or area first solves for the radius, then derives everything else from it:

$$r = \frac{d}{2} \qquad r = \frac{C}{2\pi} \qquad r = \sqrt{\frac{A}{\pi}}$$

Worked Example

A circle with a radius of 5 units:

1. Diameter: $d = 2 \times 5 = 10$.
2. Circumference: $C = 2\pi \times 5 \approx 31.42$.
3. Area: $A = \pi \times 5^{2} \approx 78.54$.