How to Find the Radius From the Circumference (With Examples)

The radius is the distance from the centre of a circle to its edge, and if you know the circumference — the distance all the way around — you can find the radius with one short formula: r = C ÷ (2π). Divide the circumference by 2π and you’re done. Here’s exactly how it works, step by step.

The formula: r = C ÷ (2π)

This comes straight from the circumference formula, C = 2πr. That formula builds the circumference from the radius. To go the other way — from circumference back to radius — you just undo it by dividing by 2π:

• r is the radius you’re solving for.
• C is the circumference (the distance around).
• π (pi) is about 3.14159, so 2π is about 6.28318.

Step by step

1. Take your circumference.
2. Divide it by 2π (about 6.28318).
3. The answer is your radius.

Example — circumference of 31.42 cm:

• 31.42 ÷ 6.28318 ≈ 5

So the radius is about 5 cm.

Example — circumference of 18.85 cm:

• 18.85 ÷ 6.28318 ≈ 3

So the radius is about 3 cm.

Getting the diameter too

The diameter goes all the way across the circle and is always exactly twice the radius. So once you have the radius, just double it — or divide the original circumference by π instead of 2π:

• diameter = 2 × radius, or diameter = C ÷ π

For the first example, the diameter is 5 × 2 = 10 cm.

Quick reference

Radius for a few common circumferences (using π ≈ 3.14159):

Circumference	Radius
6.28	1
12.57	2
18.85	3
31.42	5
62.83	10

Do it instantly

You don’t have to divide by hand. Our free circle calculator gives you the radius, diameter, and area the moment you type in the circumference — with unit conversion built in.

Frequently asked questions

What is the formula to find the radius from the circumference?

r = C ÷ (2π). Divide the circumference by 2π (about 6.28318) and the result is the radius.

How do you find the radius if the circumference is 31.42?

Divide 31.42 by 2π: 31.42 ÷ 6.28318 ≈ 5. So the radius is about 5.

How do you go from circumference to diameter instead?

Divide the circumference by π (about 3.14159). The diameter is always twice the radius, so you can also just double the radius.

Why do you divide by 2π and not just π?

Because the circumference formula is C = 2πr. To undo it and get r on its own, you divide both sides by 2π.

What units is the radius in?

The radius comes out in the same unit as the circumference. If the circumference is in centimetres, the radius is in centimetres too.