What is the formula for the perimeter of a circle?

The perimeter of a circle is called its circumference. The formula is C = 2πr, where r is the radius, or equivalently C = πd where d is the diameter. Using the mathematical constant π (approximately 3.14159265), a circle with a radius of 5 cm has a circumference of 2 × 3.14159 × 5 = 31.416 cm.

What is the difference between circumference and perimeter of a circle?

There is no difference. The word 'perimeter' describes the total boundary length of any two-dimensional shape. For a circle specifically, this boundary is called the circumference. The two terms are used interchangeably when referring to a circle: circumference = perimeter = 2πr.

How do I find the perimeter of a circle if I only know the area?

If you know the area A of a circle, first find the radius using r = √(A / π), then calculate the circumference using C = 2πr. For example, if the area is 78.54 cm², the radius is √(78.54 / 3.14159) = √25 = 5 cm, and the circumference is 2 × 3.14159 × 5 = 31.42 cm.

Circle Perimeter Calculator

This calculator works out the perimeter, more commonly called the circumference, of a circle from either its radius or its diameter. Knowing the circumference is useful whenever you need a length rather than an area, such as fencing a circular garden bed, ordering trim or edging, working out how far a wheel travels in one revolution, or measuring a pipe for lagging or labelling. To use it, choose whether you are entering a radius or a diameter, type in that measurement, and select the unit you are working in, from millimetres to kilometres, or inches, feet and yards. The calculator instantly applies the standard formula, C = 2πr or equivalently C = πd, using the full precision value of π built into JavaScript. Alongside the perimeter it returns the matching radius, diameter and area, so you can check every measurement of the circle at a glance. The detail panel shows which formula was used and the resulting circumference to four decimal places. For example, a radius of 5 cm gives a diameter of 10 cm, a circumference of 31.4159 cm and an area of 78.5398 cm². Because this is geometry rather than a real-world estimate, the result is exact for the figure you enter, so accuracy depends only on how precisely you measure the radius or diameter of the actual circle.

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Standard formula Uses the exact value of π (Math.PI in JavaScript, 15 significant figures). Result rounded to 4 decimal places.

1. Circle Measurement

Input type

Radius (r)

units

Diameter (d = 2r)

units

Unit of measurement

2. Results at a Glance

Radius (r)-

Diameter (d)-

Formula usedC = 2πr

Perimeter (C)-

Area (A = πr²)-

Circle Perimeter

Radius

Perimeter (Circumference)
-
-

Diameter

Area

Worked Example (default values)

Radius r = 5 cm
Diameter d = 2 × 5 = 10 cm
Perimeter C = 2 × π × 5 = 31.4159 cm
Area A = π × 5² = 78.5398 cm²

How to Calculate the Perimeter of a Circle

The perimeter of a circle is more commonly called the circumference. It is the total distance around the outside of the circle. The formula uses π (pi), the mathematical constant approximately equal to 3.14159265358979.

There are two equivalent formulas depending on what measurement you have:

Known value	Formula	Example (r = 5 cm)
Radius (r)	C = 2πr	C = 2 × 3.14159 × 5 = 31.4159 cm
Diameter (d)	C = πd	C = 3.14159 × 10 = 31.4159 cm

Both formulas give the same result because the diameter equals twice the radius (d = 2r). This calculator accepts either input and works out the other automatically.

Radius vs Diameter

The radius is the distance from the centre of the circle to any point on its edge. The diameter is the straight-line distance across the circle through its centre, which is always exactly twice the radius. When measuring a circular object physically, it is often easier to measure the diameter directly (for example, with callipers across a pipe) and then divide by two to get the radius.

Circle Area vs Perimeter

The perimeter (circumference) measures the length of the boundary of the circle, expressed in the same units as the radius (e.g., cm, m). The area measures the flat space enclosed by the circle, expressed in square units (e.g., cm², m²). The two are related: A = πr², and C = 2πr. You can derive the radius from either measurement and then calculate the other.

Practical Uses

Fencing, edging, or trim around circular garden beds or pools
Calculating the length of a belt, rope, or wire that wraps around a circular drum or wheel
Determining how far a wheel travels per revolution (tyre circumference)
Measuring pipe circumference for lagging, cladding, or labelling
Geometry problems involving circles, sectors, and arcs

Common Circle Perimeters

Radius	Diameter	Circumference	Area
1 cm	2 cm	6.2832 cm	3.1416 cm²
5 cm	10 cm	31.4159 cm	78.5398 cm²
10 cm	20 cm	62.8318 cm	314.1593 cm²
1 m	2 m	6.2832 m	3.1416 m²
5 m	10 m	31.4159 m	78.5398 m²
10 m	20 m	62.8318 m	314.1593 m²

Related Calculators

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Circumference Calculator: focused circumference tool with unit conversions.
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Arc Length and Sector Area Calculator: calculate arc length and sector area for a given angle.
Area Calculator: area for rectangles, triangles, and other common shapes.

Sources and method: Formula C = 2πr is standard Euclidean geometry. π value: Math.PI (IEEE 754 double precision, 15 significant figures). See NZQA Level 1 Mathematics (AS91029) for curriculum context.

This calculator uses the standard geometric formula for a perfect circle. Results are rounded to 4 decimal places. For very large or very small measurements, use consistent units throughout to avoid conversion errors.