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
| Area | A = a ∙ b | ||||
| Perimeter | P = 2 ∙ a + 2 ∙ b | ||||
| Diagonal length | d = a² + b² | ||||
| Circumradius | R =
|
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.
Example:
For the side lengths a and b, a = 3 cm and b = 2 cm. We are looking for the area A:
A=a∙b=3 cm∙2 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 |
| 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:
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.
| P |
| 2 |
| P |
| 2 |
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:
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:
Circumradius
A circumcircle of a rectangle is a circle where all 4 corners of the rectangle lie on the circle. The diagonals of the rectangle are exactly as long as the diameter of the circumcircle. Thus, the radius R of the circumcircle can be calculated by dividing the diagonal length d by 2.
| d |
| 2 |