How circumference is calculated
Circumference is the distance once around a circle, and it is always π times the diameter.
C = 2 × π × r = π × d
- From the radius: multiply by 2, then by π. C = 2πr.
- From the diameter: multiply by π. C = πd.
- From the area: divide by π and take the square root to get the radius, then use C = 2πr.
- From the circumference: divide by π for the diameter, and by 2π for the radius.
- For a wheel, one full turn rolls forward one circumference, so 100 turns cover 100 × C.
Worked example — A circle with a 5 cm radius: C = 2 × π × 5 = 31.4159 cm. A 26 inch bike wheel: C = π × 26 = 81.6814 in, so 100 turns cover about 680.68 ft.
Common circle and wheel sizes
| Diameter | Measured in | Circumference |
|---|---|---|
| 10 cm | Centimetres | 31.4159 cm |
| 30 cm | Centimetres | 94.2478 cm |
| 1 m | Metres | 3.1416 m |
| 26 in | Inches | 81.6814 in |
| 12 in | Inches | 37.6991 in |
| 50 cm | Centimetres | 157.0796 cm |
Swipe the table sideways to see the rest.
Each row starts from the diameter.
Things to consider
- Measure across the widest part of the circle for the diameter.
- To measure a tree, pipe or post, wrap a string around it, mark it, then lay it flat against a ruler.
- For a car or bike tyre, measure the diameter with the tyre fitted and inflated.
- Doubling the diameter doubles the circumference, but makes the area four times bigger.
Frequently asked questions
What is the formula for circumference?
C = 2πr, or C = πd. A circle with a 5 cm radius has a circumference of about 31.4159 cm.
How do I find the circumference from the diameter?
Multiply the diameter by π. A 10 cm diameter gives 10 × 3.14159 = 31.4159 cm.
How do I find the diameter from the circumference?
Divide the circumference by π: d = C ÷ π. A 31.4159 cm circumference gives a 10 cm diameter.
How do I find the area from the circumference?
Find the radius with r = C ÷ 2π, then A = πr². Or use the Area of a Circle Calculator, which accepts the circumference directly.
Is circumference the same as perimeter?
Yes, for a circle. Circumference is the special name for the perimeter of a circle.
What is π?
Pi is the ratio of any circle's circumference to its diameter, about 3.14159. It never ends or repeats; this calculator uses it to full precision.
Results are estimates for general information only, not financial, medical or professional advice.