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Circle Calculator

Get every measurement of a circle from any single one with this free circle calculator. Enter the radius, diameter, circumference or area — whichever one you know — and it works out the other three instantly, showing the formula and substitution behind each answer. Useful for everything from pizza sizes and pipe diameters to garden plots and school geometry.

How to use

1. Choose which measurement you already know — radius, diameter, circumference or area — from the “I know the” list.
2. Type its value, and pick the unit (centimetres, metres, inches and more). The unit is only a label; it does not change the maths.
3. Press Calculate. The area appears in big type, with the radius, diameter and circumference underneath.
4. Check the “Formulas used” box to see each formula with your own numbers substituted in — ideal for homework.

Radius, diameter, circumference and area — reference

Notice the radius-2 row: circumference and area are both 12.5664 — a famous coincidence that happens only at r = 2.

How it works

Everything about a circle hangs off one length: the radius, the distance from the centre to the edge. The diameter is simply twice the radius — the longest straight line across the circle, passing through the centre. The circumference, the distance all the way around, is π times the diameter, or 2πr. And the area, the space inside, is π times the radius squared. Know any one of the four and the radius is either given, a halving, a division by 2π, or a square root away — after which the other three follow at once. That is all this calculator does, in whichever direction you need.

The constant π (pi) is the ratio of any circle’s circumference to its diameter — about 3.14159 — and it is the same for every circle ever drawn, from a coin to a planet’s orbit. It is an irrational number, so all circumference and area answers are rounded; this page gives four decimal places, far more than any tape measure can check.

The four values grow at very different rates, which catches people out. Double the radius and the circumference doubles too — but the area quadruples, because the radius is squared inside it. That is why a 14-inch pizza is not twice a 7-inch pizza but four times as much food, and why a slightly wider pipe carries so much more water. The reference table above shows the pattern: at radius 14 the circumference is 87.9646 while the area has raced ahead to 615.7522.

Everyday uses are everywhere: checking how much fencing a round garden bed needs (the circumference), how much paint or turf covers a circular plot (the area), whether a round table of a given diameter fits a room, or what length of pipe, rope or wire matches a drum’s wrap. If someone gives you only the distance around a tree trunk, this page can even give you its thickness — circumference in, diameter out.

Worked example

A round rug has a radius of 7 cm in a scale drawing (the same numbers work for any unit). Find its diameter, circumference and area.

Step 1: Diameter = 2 × radius = 2 × 7 = 14.
Step 2: Circumference = 2 × π × radius = 2 × π × 7 = 43.9823.
Step 3: Area = π × radius² = π × 49 = 153.938.

Going the other way works too: an area of 78.5398 means the radius is √(78.5398 ÷ π) = 5, a standard result in the table above. The calculator opens with radius 7 entered, so the big answer reads Area = 153.938 cm² with 14 and 43.9823 underneath.

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