Perimeter of a Circle Formulas & Calculator

The perimeter of a circle can be calculated using one of the following 3 formulas: one if you know the circle radius, another if you know the diameter and finally another if you know the area of the circle.

Formula Knowing the Radius

If you know the radius of the circle (the line from the center to the edge), you can calculate its perimeter using the following formula:

Circle Perimeter

$circumference = π \cdot 2 \cdot R$ $"circumference" = pi * 2 * R$

Circle Radius

Circumference Result

Where:

$π = 3.141592653589$ $pi = 3.141592653589$
$R = circle radius$ $R = "circle radius"$

Formula Knowing the Diameter

If you know the diameter of the circle (the line that crosses the circle edge to edge through the center), you can calculate its perimeter using the following formula:

Circle Perimeter

$circumference = π \cdot D$ $"circumference" = pi * D$

Circle Diameter

Circumference Result

Where:

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$π = 3.141592653589$ $pi = 3.141592653589$
$D = circle diameter$ $D = "circle diameter"$

Formula Knowing the Area

If you know the area of a circle circle (the content space inside the circle), you can calculate its perimeter using the following formula:

Circle Perimeter

$circumference = \sqrt{4 \cdot π \cdot A}$ $"circumference" = sqrt(4 * pi * A)$

Circle Area

Circumference Result

Where:

$π = 3.141592653589$ $pi = 3.141592653589$
$A = circle area$ $A = "circle area"$

Formula Knowing the Circumference

If you know the circumference of the circle (perimeter), you can calculate its radius using the following formula:

Circle Perimeter

$R = \frac{circumference}{2 \cdot π}$ $R = "circumference" / (2 * pi)$

Circle Circumference

Circumference Result

Where:

$π = 3.141592653589$ $pi = "3.141592653589"$
$R = circle radius$ $R = "circle radius"$

Circle Definition

A circle is a shape or figure that is plane (2 dimensions) and perfectly round, with all points in the edge equidistant from the center.

The circle is a very basic geometric shape and a very common appearance in nature.

Circumference Definition

The circumference is the perimeter of a continuously curved shape, including a circle. It is the line around the curved shape that marks its boundary.

See perimeter.

Perimeter Definition

A perimeter is defined by the outer path of a shape. The shape is always in 2 dimensions. The perimeter is the total length of the exterior path. Another way of looking at this is to think of it as the boundary length of a shape.

In the case of a circle, the perimeter is called a circumference.

Perimeter has a Greek origin, "peri" means "around", and "meter" means "measure". So perimeter means "measure around".

Formula Definition

It is a representation of a rule or a general principle using letters. (Algebra, A. Baldor)
When describing formulas in plural, it is also valid to say "formulae".

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