Area Index

Area of a Circle Formulas & Calculator

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

Circle Area and Perimeter

Formula Knowing the Radius

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

Circle Area

$$"area" = pi * R^2$$

Circle Radius

Area Result

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Where:

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

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 area using the following formula:

Circle Area

$$"area" = (pi/4) * D^2$$

Circle Diameter

Area Result

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Where:

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

Formula Knowing the Perimeter

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

Circle Perimeter

$$"area" = P^2 / (4 pi)$$

Circle Perimeter

Area Result

Copy paste the following code into your website HTML to display this formula and its calculator.

Our calculators are free to use and mobile friendly. By using them you agree to give attribution to "© WikiFormulas.com". A link is optional but appreciated. Thank you!

Where:

$$pi = "3.141592653589"$$
$$P = "circle perimeter"$$

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.

Area Definition

It is the space of the internal surface in a figure, it is limited for the perimeter. Also, the area can be calculated in a plane of two dimensions.

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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