What is the formula for the circumference of a circle?

The circumference of a circle is calculated using C = 2πr (where r is the radius) or equivalently C = πd (where d is the diameter). Pi (π) is the constant approximately equal to 3.14159. For example, a circle with a radius of 5 cm has a circumference of 2 × 3.14159 × 5 = 31.416 cm.

How do I find the radius from the circumference?

Rearrange C = 2πr to get r = C / (2π). For example, if the circumference is 31.416 cm, the radius is 31.416 / (2 × 3.14159) = 5 cm. The diameter is simply twice the radius: d = C / π.

What is the difference between circumference and perimeter?

Circumference is the specific term for the perimeter of a circle. Perimeter is the general term for the total boundary length of any closed shape. For a circle, circumference and perimeter refer to the same measurement: the total distance around the outside of the circle.

Circumference Calculator

This calculator finds the circumference, area, diameter and radius of any circle from a single known measurement, using the standard formulas C = 2πr and A = πr². Start by choosing what you already know, radius, diameter or circumference, then enter that value, pick a unit of measurement from millimetres up to miles, or generic units, and choose how many decimal places to show. The calculator instantly returns all four circle properties in a results panel, with the circumference highlighted, plus a step-by-step breakdown showing your input value alongside the calculated radius, diameter, circumference and area. A second panel shows the circumference as an exact multiple of pi, the pi value used, and the constant ratios of circumference to diameter, always pi, and circumference to radius, always two pi. This makes it useful for wheel and tyre sizing, pipe and cylinder measurements, sewing and craft patterns, circular pools and tanks, fencing or edging materials, and any situation where you need to work forward from a radius or diameter, or backward from a known circumference to find the radius. Because the maths is exact, results are limited only by the rounding you choose, so increase the decimal places if you need more precision.

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Standard formula C = 2πr | A = πr² | Works for any unit of length.

1. Known Measurement

What do you know?

Radius (half the width of the circle)

units

Please enter a positive number.

Diameter (full width of the circle)

units

Please enter a positive number.

Circumference (distance around the circle)

units

Please enter a positive number.

2. Options

Unit of measurement

Decimal places

Circle Properties

Circumference
-
C = 2πr

Area

A = πr²

Diameter

d = 2r

Radius

r = C / (2π)

Step-by-Step Calculation

Input value-

Radius (r)-

Diameter (d = 2r)-

Circumference (C = 2πr)-

Area (A = πr²)-

In Other Units

Circumference (exact fraction)-

Pi used3.14159265358979...

C / d ratioπ (always)

C / r ratio2π (always)

Area / r² ratioπ (always)

Circumference Formula

The circumference of a circle is the total distance around its outer edge. There are two equivalent formulas depending on which measurement you have:

From radius: C = 2πr
From diameter: C = πd (since d = 2r)

Pi (π) is a mathematical constant approximately equal to 3.14159265. It represents the ratio of any circle's circumference to its diameter, and this ratio is always exactly π, regardless of the size of the circle.

Worked Example

For a circle with a radius of 5 cm:

Property	Formula	Result
Radius	Given	5 cm
Diameter	d = 2r = 2 × 5	10 cm
Circumference	C = 2πr = 2 × 3.14159 × 5	31.416 cm
Area	A = πr² = 3.14159 × 5²	78.540 cm²

These are the values the calculator shows with its default inputs (radius = 5 cm, 3 decimal places).

Working Backwards from Circumference

If you know the circumference and need to find the radius or diameter, rearrange the formula:

Radius: r = C / (2π)
Diameter: d = C / π

For example, a circumference of 31.416 cm gives a radius of 31.416 / (2 × 3.14159) = 5 cm.

Area of a Circle

The area enclosed by a circle is A = πr². This is a separate measurement from circumference. Circumference is a length (one-dimensional), while area is a square measurement (two-dimensional). For a 5 cm radius circle, the area is π × 25 = 78.540 cm².

Circumference in Real Life

Circumference calculations come up in many practical situations:

Wheel and tyre fitting: knowing the circumference of a tyre helps calculate how far a vehicle travels per revolution.
Pipe and cylinder sizing: the circumference of a pipe determines how much material is needed to wrap or insulate it.
Sewing and craft: cutting fabric in a circle requires knowing the circumference for the outer edge.
Construction: circular pools, tanks, or roundabouts involve circumference for edging or fencing materials.
Astronomy: the circumference of the Earth (approximately 40,075 km at the equator) is derived from C = 2πr.

Related Calculators

Method: Standard Euclidean geometry. Circumference C = 2πr; area A = πr²; diameter d = 2r. Pi is computed using JavaScript's built-in Math.PI constant (15 significant figures).

This calculator works for any unit of length. Area results are in square units of whatever length unit you enter. Results are rounded to the number of decimal places you select.