Rectangle Perimeter Calculator

What is the perimeter of a rectangle?

The perimeter of a rectangle is the total length of its four sides. A rectangle has two pairs of equal sides, usually called length and width. This calculator finds the perimeter when a length and a width are entered.

Rectangle perimeter formula

The formula is:

$P = 2 \times (L + W)$

Here, $P$ is the perimeter, $L$ is the length of one pair of sides, and $W$ is the length of the other pair. A rectangle has four sides in total: two of length $L$ and two of length $W$. Adding all four gives $L + W + L + W$, which is the same as $2 \times (L + W)$.

Length and width just name the two different side lengths. Neither one has to be the longer side; the formula gives the same result either way.

How to calculate rectangle perimeter

1. Measure or note the length of one side.
2. Measure or note the length of the adjacent side (the width).
3. Add the two numbers together.
4. Multiply the sum by 2.

Both measurements must use the same unit before adding them. Mixing feet and inches, or meters and centimeters, gives a wrong answer.

To use the calculator, enter a length and a width, in any matching units. The perimeter appears immediately, along with the formula filled in with the entered numbers. A small diagram shows the rectangle's shape. Both length and width must be greater than zero; entering zero or a negative number triggers an error message instead of a result.

Example

A room measures 12 feet by 10 feet. Its perimeter is:

$P = 2 \times (12 + 10) = 2 \times 22 = 44 \text{ feet}$

A garden plot measures 8 meters by 5 meters. Its perimeter is:

$P = 2 \times (8 + 5) = 2 \times 13 = 26 \text{ meters}$

Perimeter versus area

Perimeter and area measure different things. Perimeter is a distance: the length of the boundary around a shape. Area is the amount of surface a shape covers. For a rectangle, area is $A = L \times W$, not $2 \times (L + W)$.

A fence needs a perimeter measurement, since fencing runs along the boundary. Flooring or paint needs an area measurement, since it covers the surface. The two values do not stay in a fixed relationship: a 1-by-1 square has a perimeter of 4 and an area of 1, but a 10-by-10 square has a perimeter of 40 and an area of 100.

Perimeter of a square

A square is a rectangle with all four sides equal. Its perimeter formula simplifies to:

$P = 4 \times s$

where $s$ is the length of one side. This is the same as the rectangle formula with $L$ and $W$ both equal to $s$.

Frequently asked questions

What is the formula for the perimeter of a rectangle?

$P = 2 \times (L + W)$, where $L$ and $W$ are the lengths of two adjacent sides.

What is the difference between perimeter and area?

Perimeter is the distance around the outside of a shape. Area is the amount of surface it covers. For a rectangle, perimeter is $2 \times (L + W)$ and area is $L \times W$.

What units does the result use?

The same unit used for length and width. If both are entered in meters, the perimeter is in meters. If both are in feet, the perimeter is in feet.

Does it matter which side is called length and which is called width?

No. Swapping the two labels gives the same perimeter, since the formula only adds them together.

How is a square's perimeter calculated?

A square is a rectangle with equal sides, so its perimeter is $4 \times s$, where $s$ is one side length.

What if the length and width are in different units?

Convert both to the same unit first. For example, 12 feet and 60 inches should become 12 feet and 5 feet before adding, since 60 inches equals 5 feet.

References

1. Weisstein, Eric W. "Rectangle." MathWorld — A Wolfram Web Resource. https://mathworld.wolfram.com/Rectangle.html
2. Euclid. Elements, Book I. Translated by Sir Thomas L. Heath, Dover Publications, 1956.