Circumference Calculator
Calculate the circumference and area of a circle from the radius or diameter.
Also find the radius or diameter from a known circumference.
What Is Circumference?
The circumference is the distance around the outside of a circle — its perimeter. If you unrolled the edge of a circle into a straight line, the circumference is how long that line would be.
The Formulas
From the radius (r):
C = 2πr
From the diameter (d):
C = πd
To find radius from circumference:
r = C / (2π)
To find diameter from circumference:
d = C / π
Area of a circle:
A = πr²
The Number Pi (π)
π (pi) is the ratio of any circle’s circumference to its diameter. It is constant for every circle, regardless of size. π is an irrational number — its decimal expansion never ends and never repeats:
π ≈ 3.14159265358979…
The history of π spans thousands of years:
- Archimedes of Syracuse (287–212 BC) was the first to rigorously calculate π, using inscribed and circumscribed polygons, determining it lies between 3 10/71 and 3 1/7 (approximately 3.1408 to 3.1429)
- William Jones first used the Greek letter π for this ratio in 1706
- Leonhard Euler popularized the notation in 1737
Today, π has been calculated to over 100 trillion decimal places, though only 39 digits are needed to calculate the circumference of the observable universe to the accuracy of a hydrogen atom.
Radius vs. Diameter
- Radius: distance from the center to the edge
- Diameter: distance across the full circle through the center
- Always:
d = 2r
Practical Applications
- Tire circumference: A car tire with a 14-inch radius has C = 2π × 14 ≈ 87.96 inches per revolution. This is how your odometer calculates distance.
- Circular garden: A circular garden bed with a 3-meter radius has a circumference of about 18.85 meters — the length of edging you need to buy.
- Pipes and tubes: The circumference of a pipe tells you how much material wraps around it.
- Wheel rotations: Circumference ÷ distance = number of wheel rotations needed.
Unit Conversion Reference
| Unit | Conversion |
|---|---|
| 1 meter | 100 cm |
| 1 inch | 2.54 cm |
| 1 foot | 30.48 cm |
| 1 foot | 12 inches |
Worked Example
A circle has a radius of 5 inches:
- Circumference = 2 × π × 5 = 31.416 inches
- Diameter = 2 × 5 = 10 inches
- Area = π × 5² = 78.540 square inches
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.