Circumference of a Circle Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the circumference of a circle?

Answer

Circumference of a circle
C = 2 · π · r

Here r is the radius. The result comes out in units.

Where the formula comes from

C = 2 · π · r

π is defined as the ratio of a circle’s circumference to its diameter — that is what the number means. So C = π·d, and since d = 2r, C = 2πr. The formula is not derived from π; π is derived from it.

Worked examples

Let r = 5. Then the circumference of a circle ≈ 31.42 units.

Let r = 3.2. Then the circumference of a circle ≈ 20.11 units.

The common mistake

Asking for the "perimeter of a circle" and expecting a different formula. It is the same length under a different name — a circle’s perimeter IS its circumference, 2πr.

Other quantities: Circle

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the circumference of a circle? (The answer is: C = 2 · π · r). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula

If r =Circumference
1≈ 6.28 units
2≈ 12.57 units
3≈ 18.85 units
4≈ 25.13 units
5≈ 31.42 units
10≈ 62.83 units

FAQ

What is the formula for the circumference of a circle?

Circumference of a circle C = 2 · π · r

Where does this formula come from?

π is defined as the ratio of a circle’s circumference to its diameter — that is what the number means. So C = π·d, and since d = 2r, C = 2πr. The formula is not derived from π; π is derived from it.

What is the most common mistake here?

Asking for the "perimeter of a circle" and expecting a different formula. It is the same length under a different name — a circle’s perimeter IS its circumference, 2πr.

How do I use this formula?

Put your own numbers in place of the letters. With r = 3.2, for instance, the formula C = 2 · π · r gives ≈ 20.11 units.