Circumference Calculator

Enter the radius or diameter of a circle and get its circumference — the distance all the way around — with step-by-step work.

Radius

— or —

Diameter

How to Calculate Circumference

The circumference is the distance around the outside of a circle — its perimeter. There are two equivalent formulas depending on whether you know the radius or diameter:

$$C = 2\pi r \qquad \text{or} \qquad C = \pi d$$

Both give the same result because $d = 2r$.

Step-by-Step: Finding Circumference from Radius

Find the circumference of a circle with radius $r = 6$.

Step 1 — Write the formula:

$$C = 2\pi r$$

Step 2 — Substitute the radius:

$$C = 2 \times \pi \times 6$$

Step 3 — Multiply:

$$C = 12\pi \approx 37.6991\ \text{units}$$

Step-by-Step: Finding Circumference from Diameter

Find the circumference of a circle with diameter $d = 14$.

Step 1 — Write the formula:

$$C = \pi d$$

Step 2 — Substitute the diameter:

$$C = \pi \times 14 = 14\pi \approx 43.9823\ \text{units}$$

Reference Table

Radius	Diameter	Exact Circumference	Decimal
1	2	$2\pi$	6.2832
2	4	$4\pi$	12.5664
3	6	$6\pi$	18.8496
5	10	$10\pi$	31.4159
10	20	$20\pi$	62.8318

Frequently Asked Questions

What is the difference between circumference and perimeter?

They're the same concept — the distance around the outside of a shape. Circumference is the specific word used for circles; perimeter is used for polygons (triangles, squares, etc.).

What is $\pi$?

Pi ($\pi$) is the ratio of any circle's circumference to its diameter. It is the same for every circle, regardless of size. Its decimal expansion starts with 3.14159265… and continues infinitely without repeating.