Circle Calculator

Enter any one value — radius, diameter, circumference, or area — to calculate the rest.

The formulas behind a circle

Every measurement of a circle traces back to its radius through π: diameter is twice the radius (D=2R), circumference is 2πR, and area is πR². Enter any single one of the four values above, and the other three follow automatically.

Why π shows up everywhere

π is defined as the ratio of a circle's circumference to its diameter — a constant that holds true for every circle, regardless of size. It's an irrational number (its decimal digits never terminate or repeat), which is why it's always approximated (as 3.14159… or 22/7) rather than written exactly.

Circumference measures the distance around a circle; area measures the space inside it. They scale differently with radius — circumference grows linearly with R, while area grows with R², so doubling the radius quadruples the area but only doubles the circumference.

Common questions

What if I only know the area?

Solve for radius first: R = √(A/π), then use that radius to find the diameter and circumference — exactly what this calculator does automatically.

Why can I only enter one value?

Because all four measurements are mathematically linked through the radius — entering more than one risks contradictory inputs (a radius and area that don't actually match the same circle).

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