# Rectangles - Calculator given values:
= =
calculated values:

With this calculator you can calculate the area, perimeter, diagonal length and circumradius of a rectangle. You can select to how many decimal places the calculation should be rounded. The calculator always uses the rounded values for further calculations.

## Formulas AreaA = a ∙ b
PerimeterP = 2 ∙ a + 2 ∙ b
Diagonal lengthd = a² + b²
 d 2
=
 a² + b² 2

## What is a rectangle?

A rectangle is a quadrilateral where all 4 interior angles are right angles. Opposite sides have the same side lengths and are parallel to each other. ## Area of a rectangle

If two sides each have side length a and the other two each have side length b, then you can calculate the area by multiplying a and b.

A=ab

Example: For the side lengths a and b, a = 3 cm and b = 2 cm. We are looking for the area A:

A=ab=3 cm2 cm=6 cm²

If you know the area and either the side length a or the side length b and want to calculate the other side length, you can calculate this as follows:

a=
 A b
or b=
 A a

## Perimeter of a rectangle

To calculate the perimeter of a rectangle, the lengths of all 4 sides must be added together. If the side lengths are a and b, then the perimeter P is:

P=2a+2b

Example:

For the side lengths a and b, a = 2 cm and b = 3 cm. We are looking for the perimeter P:

 P = 2 ∙ a + 2 ∙ b = 2 ∙ 2 cm + 2 ∙ 3 cm = 4 cm + 6 cm = 10 cm

If the perimeter and one of the side lengths are known, the other side length can be calculated by solving the equation for a or b, respectively.

a=
 P 2
b
or b=
 P 2
a

## Diagonal length Diagonals are drawn in a rectangle by drawing a line from one angle of the rectangle to the opposite angle. The length of this line is the diagonal length.

If you draw a diagonal into a rectangle with side lengths a and b, this creates 2 right triangles. For both triangles, the diagonal length d is the length of the hypotenuse, and for both triangles, the legs have side lengths a and b. The diagonal length d can now be calculated with the Pythagorean theorem:

d=a² + b²

Example:

A rectangle has the side lengths a = 3 cm and b = 2 cm. The diagonal length d is to be calculated. d = a² + b² = (3 cm)² + (2 cm)² = 9 cm² + 4 cm² = 13 cm² ≈ 3.605551 cm

If you know d and either a or b, then to calculate the other side you can transform the equation as follows:

a=d² − b² or b=d² − a² 