Circumference Calculator

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

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