## Properties of a Rectangle

This tool calculates the basic geometric properties of a rectangle. Enter below the shape dimensions. The calculated results will have the same units as your input. Please use consistent units for any input.

a = | |||

b = | |||

Geometric properties: | |||

Area = | |||

Perimeter = | |||

Diagonal p = | |||

Inradius R _{i} = | |||

Circumradius R _{c} = |

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## Definitions

### Geometry

Rectangle is a quadrilateral shape with two pairs of parallel sides, that meet each other at right angles. If all sides are equal the shape is a square. The area of a rectangle is given by the formula:

where a, b the lengths of the sides.

The perimeter of a rectangle is simply the sum of the lengths of all sides:

The length of the diagonal, can be expressed in terms of the length of the sides, using the Pythagorean theorem on the right triangle with the diagonal as hypotenuse:

It is not possible to inscribe a circle on a rectangle, that is tangent to all four sides, unless these are equals (shape is square). The largest circle, that can be enclosed to the shape, has a radius equal to:

On the other hand, there is a circumscribed circle (a circle that passes through all vertices) for any rectangle. Its radius is equal to:

where p the diagonal length.