## 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 Ri = Circumradius Rc =

## 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:

$A = a b$

where a, b the lengths of the sides.

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

$P = 2\left(a+b\right)$

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:

$p = \sqrt{a^2 + b^2}$

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:

$R_i = \frac{\min{\left(a;b\right)}}{2}$

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

$R_c = \frac{p}{2} = \frac{\sqrt{a^2 + b^2}}{2}$

where p the diagonal length.