Circumference Formula
The circumference of a circle is the distance around its edge. There are two equivalent ways to calculate it, depending on which measurement you already know:
- Using radius: C = 2πr
- Using diameter: C = πd
Where C is circumference, r is radius, d is diameter, and π ≈ 3.141592653589793.
Circle Circumference Equation
The base equation is C = 2πr. Since the diameter is always twice the radius (d = 2r), the same equation can be rewritten as C = πd — both describe the same circle.
- Know the radius → use C = 2πr
- Know the diameter → use C = πd
How to Calculate the Circumference of a Circle
If you know the radius
- Measure the radius.
- Multiply the radius by 2.
- Multiply the result by π.
Example: r = 7 cm → C = 2π(7) ≈ 43.98 cm
If you know the diameter
- Measure the diameter.
- Multiply the diameter by π.
Example: d = 14 cm → C = π(14) ≈ 43.98 cm
Radius vs Diameter
- The radius goes from the center of the circle to its edge.
- The diameter goes all the way across the circle, through its center.
- Diameter = 2 × radius (d = 2r)
- Radius = diameter ÷ 2 (r = d / 2)
Reverse Calculations
How to Find Radius From Circumference
r = C / (2π)
Example: C = 62.83 cm → r ≈ 10 cm
How to Find Diameter From Circumference
d = C / π
Example: C = 62.83 cm → d ≈ 20 cm
Accuracy & π
π (pi) is approximately 3.141592653589793. This calculator uses full-precision π for every calculation rather than rounding π to 3.14 first — rounding is applied only to the final displayed result, so the answer stays as accurate as possible.
Circumference is a length, so it always uses the same unit as the radius or diameter you entered: radius in cm gives circumference in cm, radius in inches gives circumference in inches, and so on.
Common Circumference Calculation Mistakes
- Using diameter in the radius formula. C = 2πr requires the radius. If you only know the diameter, use C = πd instead.
- Using radius as if it were diameter. Remember d = 2r — don't plug the radius into a formula expecting the diameter.
- Using π = 3.14 unnecessarily. This calculator uses full π precision and only rounds the displayed result.
- Mixing units. Convert every measurement to the same unit before calculating by hand.