Circumference of a Circle
Calculate the circumference of a circle using C = 2πr or C = πd.
Find the distance around any circle with step-by-step examples.
The Formula
C = 2 × π × r
or equivalently: C = π × d
The circumference is the total distance around the outside of a circle.
Both formulas give the same result — use whichever is more convenient based on what you know.
Variables
| Symbol | Meaning |
|---|---|
| C | Circumference (the distance around the circle) |
| π | Pi, approximately 3.14159 |
| r | Radius (distance from center to edge) |
| d | Diameter (distance across the circle through the center; d = 2r) |
Example 1
Find the circumference of a circle with radius 10 cm
C = 2 × π × r = 2 × π × 10
C = 20π
C ≈ 62.83 cm
Example 2
A bicycle wheel has a diameter of 70 cm. How far does it travel in one rotation?
C = π × d = π × 70
C ≈ 219.91 cm (about 2.2 meters per rotation)
When to Use It
Use the circumference formula when:
- Calculating the distance around circular objects (wheels, pipes, rings)
- Determining how much fencing, rope, or trim you need to go around a circle
- Finding how far a wheel travels in one revolution
- Working with circular tracks, orbits, or paths
Key Notes
- π is defined as the ratio C/d for any circle — it is not an arbitrary constant but a geometric necessity: every circle's circumference is exactly π times its diameter, which is why π appears throughout mathematics
- Circumference scales linearly with r, while area scales as r² — doubling the radius doubles the circumference but quadruples the area; this distinction matters for problems involving fencing (linear) vs covering (area)
- Arc length formula l = rθ (θ in radians) is the circumference formula applied to a fraction of the circle: a full rotation θ = 2π gives l = 2πr; a semicircle (θ = π) has arc length πr, not 2r
- Units of the result always match the radius/diameter units (linear, not squared) — circumference is a length, so cm in gives cm out; squaring the answer is the most common unit error when confusing this with area