How to find the missing length of a rectangle

Welcome to the length of a rectangle calculator, where we'll explain the formula(s) for the length of a rectangle and how to find the length of a rectangle.

Using the length of a rectangle calculator is easy — there's only two steps!

Enter the dimensions that you know of the rectangle.
Find your rectangle length in the bottom box.
The length of a rectangle calculator works both ways — try changing the rectangle's length and see how its other dimensions are affected.
Not enough to just know how to use the length of a rectangle calculator? Read on to learn how to calculate the length of a rectangle.

Depending on what information you have available, there are many ways to calculate the length of a rectangle.

If you have the area A and width w, its length w is determined as h = A/w.
If you have the perimeter P and width w, its length can be found with h = P/2−w.
If you have the diagonal d and width w, it's length is h = √(d²−w²).
If the rectangle's width is not known, you'd need to simultaneously solve the equations above to get the length h.

That's a lot of different formulas for the length of a rectangle! These are all derived from the many formulas that govern a rectangle's dimensions. Those formulas are:

$A=w×hP=2(w+h)d=w2+h2\begin{split} A &= w \times \textcolor{red}h \\ P &= 2(w+\textcolor{red}h) \\ d &= \sqrt{w^2 + \textcolor{red}h^2} \end{split}$

where:

$w$ is the rectangle's width;
$h$ is the rectangle's length;
$A$ is the rectangle's area;
$P$ is the rectangle's perimeter; and
$d$ is the length of the rectangle's diagonal, as described by the Pythagorean theorem.

A rectangle with its length

h

, width

w

, diagonal

d

, perimeter

P

, and area

A

labelled.

A rectangle has four sides. Its sides are paired, so really there are only two unique dimensions. Conventionally, the rectangle's length is the longest of these two measurements, but when the rectangle is shown to be standing on the floor, the vertical side is usually called the length.

4 m. Because the connected sides of a rectangle are perpendicular, we can use the Pythagoras theorem to work this one out.

Rearrange the Pythagoras theorem to make the rectangle's length h the subject: h = √(d²−w²).
Plug in your values: h = √(5²−3²) = √(25-9) = √16 = 4.

Updated November 03, 2020

By Chris Deziel

If you know the length and width of a rectangle, you can figure out its area. These two quantities are independent, though, so you can't do a reverse calculation and determine both of them if you know only the area. You can calculate one if you know the other, and you can find both of them in the special case in which they are equal – which makes the shape a square. If you also know the perimeter of the rectangle, you can use that information to find two possible values for length and width.

The area of a rectangle (A) is related to the length (L) and width (W) of its sides by the following relationship:

A = L \times W

If you know the width, it's easy to find the length by rearranging this equation to get

L = \frac{A}{W}

If you know the length and want the width, rearrange to get

W = \frac{A}{L}

Example: The area of a rectangle is 20 square meters, and its width is 3 meters. How long is it?
Using the expression

W = \frac{A}{L}

W = \frac{20 \text{ m}^2}{3 \text{ m}} = 6.67 \text{ m}

Because a square has four sides of equal length, the area is given by A = L2. If you know the area, you can immediately determine the length of each side, because it's the square root of the area.

Example: What are the lengths of the sides of a square with an area of 20 m2?
The length of each side of the square is the square root of 20, which is 4.47 meters.

If you happen to know the distance around the rectangle, which is its perimeter, you can solve a pair of equations for L and W. The first equation is that for area,