# Perimeter of a Rectangle Calculator

Use our perimeter of a rectangle calculator if you need to quickly estimate what is the perimeter of a specific rectangle. Try to enter some values or read on to learn more about rectangles. In the following text, we explain in detail **how to find the perimeter of a rectangle** with **10 different perimeter of a rectangle formulas**.

Rectangle is a **quadrilateral with four right angles** (4 * 90° = 360°). Its name is derived from the Latin word **rectangulus** which means right (*rectus*) angle (*angulus*). The opposite sides of rectangle are parallel to each other and of equal length. Rectangle has two diagonals which **intersect in the middle** of the rectangle and are of equal lengths. In the picture below, you can see a typical rectangle with marked parameters:

**l - length**,**w - width**,**α - angle between diagonals**,**r - circumcircle radius**,**d - diagonal**,

There are two other characteristic quantities which are not shown in the picture:

**A - area**,**P - perimeter**.

You can **always circumscribe a circle** on the rectangle because its **center is equidistant** from all of its four vertices. Moreover, the center of this circle lies exactly at the intersection of two diagonals. However, you **can't inscribe a circle** into every rectangle. In fact, you can do it only with a square which is special case of a rectangle. Square is a quadrilateral with four right angles and all four sides of equal lengths. Check out our perimeter, area and diagonal of a square calculators if you need to solve specific problems with squares!

## How to find the perimeter of a rectangle?

A perimeter is a path that surrounds any two-dimensional shape. You can think of it like a fence that is required to surround a yard of a garden. A circle is a special figure, because its perimeter is usually called the circumference.

So how to find the perimeter of a rectangle? You need to sum up the lengths of every side:

`P = l + w + l + w`

`P = 2 * l + 2 * w`

`P = 2 * (l + w)`

With this perimeter of a rectangle calculator, you can make calculations in almost any units you want. To learn more about length units, check out our length converter!

## What's the perimeter of a rectangle formula?

To calculate the perimeter in the above equations, we have used two sides of a rectangle. However, in some mathematical problems, there are **different quantities given**. How to find the perimeter of a rectangle in these situations? Most of these problems can be solved with our perimeter of a rectangle calculator. Before we write down appropriate formulas, there are three basic equations for the area, diagonal and circumcircle radius of a rectangle that you should remember:

**Area**of a rectangle:`A = w * l`

,**Diagonal**of a rectangle`d = √(l² + w²)`

,**Circumcircle radius**of a rectangle`r = d/2`

.

With the above equations we can now derive various **perimeter of a rectangle formulas** that are used by calculator on this site:

- Given
**length**and**width**:`P = 2*l + 2*w`

, - Given
**length/width**and**diagonal**:`P = 2*l + 2*√(d² - l²)`

or`P = 2*w + 2*√(d² - w²)`

, - Given
**lenght/width**and**area**:`P = 2*l + 2*A/l`

or`P = 2*w + 2*A/w`

, - Given
**length/width**and**angle**:`P = 2*l + 2*l/tan(α/2)`

or`P = 2*w + 2*w*tan(α/2)`

, - Given
**length/width**and**circumcircle radius**:`P = 2*l + 2*√(4*r² - l²)`

or`P = 2*w + 2*√(4*r² - w²)`

, - Given
**diagonal**and**area**:`P = √[2*d² + 2*√(d⁴ - 4*A²)] + √[2*d² - 2*√(d⁴ - 4*A²)]`

, - Given
**diagonal**and**angle**:`P = d * (2*sin(α/2) + 2*cos(α/2))`

, - Given
**area**and**angle**:`P = 2*√[A / tan(α/2)] * (tan(α/2) + 1)`

, - Given
**area**and**circumcircle radius**:`P = √[8*r² + 4*√(4*r⁴-A²)] + √[8*r² - 4*√(4*r⁴-A²)]`

, - Given
**angle**and**circumcircle radius**:`P = 2 * r * (2*sin(α/2) + 2*cos(α/2))`

.

Note: **The angle α between diagonals is in the front of the length** like in the first figure. Also, remember that the perimeter of a rectangle calculator assumes that the length is longer than the width!

Have you ever heard about the golden rectangle? It is a special rectangle, the side lengths of which are in golden ratio. Check out our golden rectangle calculator to learn more about constructing golden rectangles!