How do I find the circumference of a circle?

Multiply 2 × π × the radius, or π × the diameter.

About 3.14159, the ratio of any circle's circumference to its diameter.

Circle: Circumference and Area

Published 9/3/2025 · 3 min read · Everyday calculators

Lena Hoffmann — Science & education writer at OneKitly

Mathematics · Physics

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In short

A circle's circumference (the distance around) is 2 × π × radius, and its area (the space inside) is π × radius². With a radius of 5 cm: circumference = 2 × 3.14 × 5 ≈ 31.4 cm, area = 3.14 × 25 ≈ 78.5 cm². If you know the diameter instead, it's twice the radius, so circumference = π × diameter.

Circumference is 2πr, area is πr². Here's how radius, diameter and π fit together, both formulas worked through, and how not to mix them up.

Radius, diameter and π

Three things describe a circle. The radius is the distance from the centre to the edge; the diameter is all the way across through the centre, exactly twice the radius. And π (pi) is the constant that links them to the distance around: for every circle, the circumference divided by the diameter is the same number, about 3.14159. That fixed ratio is why π appears in both circle formulas — it's baked into the shape itself.

Circumference

The circumference is the length of the circle's boundary — how far you'd walk all the way around it. It's 2 × π × radius, or equivalently π × diameter, since the diameter is twice the radius. For a circle with a 5 cm radius, that's 2 × 3.14159 × 5 ≈ 31.4 cm. Because it's a length, the answer keeps ordinary units like centimetres or metres, not squared ones — a useful check that you've used the right formula.

Area

The area is the space enclosed inside the circle, and it's π × radius². Note that the radius is squared, not doubled — so a circle with a 5 cm radius has an area of 3.14159 × 5² = 3.14159 × 25 ≈ 78.5 cm². The squaring means area grows fast: doubling the radius quadruples the area. Being a two-dimensional measure, the answer is always in square units, such as square centimetres.

Don't mix them up

Two slips cause most wrong answers. The first is confusing circumference with area — remember circumference is a distance (plain units) while area is a surface (squared units), so the units themselves tell you which you've found. The second is using the diameter where the formula wants the radius: if you're given the diameter, halve it first, or switch to the diameter versions (π × d for circumference). Get the radius right and both formulas are quick and reliable.

Worked with our own calculator

Circle calculator

Given

Radius: 3

Result

Area: 28.274
Circumference: 18.85
Diameter: 6

These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.

Run it on your own figures →

Frequently asked questions

How do I find the circumference of a circle?: Multiply 2 × π × the radius, or π × the diameter.
How do I find the area of a circle?: π times the radius squared.
What is π?: About 3.14159, the ratio of any circle's circumference to its diameter.

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Sources

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