Circumference formula
The circumference is the distance around a circle. It equals pi times the diameter, or equivalently two pi times the radius. Because pi is just over three, the circumference is always a little more than three times the width of the circle.
- C = the circumference, the distance around the circle
- r = the radius
- d = the diameter, equal to 2r
- π = pi, about 3.14159
Two equivalent forms
Since the diameter is twice the radius, the two forms C = 2πr and C = πd are the same equation written differently. Use the radius version when you know the radius, and the diameter version when you know the width across. Both rely on pi, the fixed ratio of every circle circumference to its diameter.
- Take a circle with radius 5.
- Apply C = 2πr: C = 2 × 3.14159 × 5.
- C ≈ 31.42 units.
- Equivalently, the diameter is 10, and π × 10 ≈ 31.42.
Circle references
See the Circle Formula Chart for area, arc length, and more.
FAQ
What is the circumference formula?
C = 2πr, or equivalently πd, where r is the radius and d the diameter.
What is the difference between circumference and area?
Circumference is the distance around the circle (a length); area is the surface it encloses, given by πr² (a square measure).