What is the formula for the area of a rectangle?

The area of a rectangle is calculated by multiplying its length by its width: Area = length x width. For example, a rectangle that is 10 metres long and 5 metres wide has an area of 10 x 5 = 50 square metres. The result is always expressed in square units (such as m^2, cm^2, or ft^2) because you are multiplying two linear measurements together.

How do I find the perimeter of a rectangle?

The perimeter of a rectangle is the total distance around its outside edge. The formula is Perimeter = 2 x (length + width). For a rectangle that is 10 m long and 5 m wide, the perimeter is 2 x (10 + 5) = 2 x 15 = 30 metres. You can also think of it as adding all four sides: length + width + length + width.

How do I calculate the diagonal of a rectangle?

The diagonal of a rectangle is found using Pythagoras's theorem, because the diagonal forms the hypotenuse of a right-angled triangle with the length and width as the other two sides. The formula is Diagonal = sqrt(length^2 + width^2). For a 10 m x 5 m rectangle, the diagonal is sqrt(10^2 + 5^2) = sqrt(100 + 25) = sqrt(125) = 11.18 metres (to 2 decimal places).

Area of a Rectangle Calculator

This calculator works out the area, perimeter and diagonal of any rectangle from just two measurements, saving you from doing the multiplication, addition and Pythagoras by hand. Enter the length and width in your chosen unit, millimetres, centimetres, metres, kilometres, inches, feet or yards, and the results update instantly. The area (length multiplied by width) is highlighted as the headline figure, alongside the perimeter (twice the sum of length and width) and the diagonal, worked out with Pythagoras's theorem. A calculation breakdown shows each formula applied to your own numbers, and the area is automatically converted into square millimetres, square centimetres, square metres, square feet and square inches, without any manual conversion needed. A worked example using the default 10 m by 5 m rectangle shows the full method: an area of 50 m squared, a perimeter of 30 m and a diagonal of 11.18 m. Use this tool for everyday jobs such as working out how much flooring, carpet or paint to buy, how much fencing or irrigation pipe you need around a garden bed, or whether a door frame or deck is square, since equal diagonals confirm true right angles. Results are accurate for the figures you enter, but always double-check your own measurements, and consult a qualified professional for building consents, engineering drawings or legal boundary work.

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Standard Formula Area = length x width. A fundamental rule of geometry that does not change.

1. Rectangle Dimensions

Length

Width

2. Unit of Measurement

Unit

Formulae
Area = length x width
Perimeter = 2 x (length + width)
Diagonal = sqrt(length² + width²)

Results

Area
50
m²

Perimeter

Diagonal

11.18

Calculation Breakdown

Length10 m

Width5 m

Area (length x width)50 m²

Perimeter (2 x (L + W))30 m

Diagonal (Pythagoras)11.18 m

Area in Other Units

Square millimetres-

Square centimetres-

Square metres-

Square feet-

Square inches-

Worked example (default values): A rectangle is 10 m long and 5 m wide.
Area = 10 x 5 = 50 m²
Perimeter = 2 x (10 + 5) = 2 x 15 = 30 m
Diagonal = sqrt(10² + 5²) = sqrt(100 + 25) = sqrt(125) = 11.18 m

How to Calculate the Area of a Rectangle

A rectangle is a four-sided flat shape where every interior angle is 90 degrees. The two pairs of opposite sides are equal in length. Because the sides meet at right angles, calculating the area is straightforward: multiply the length by the width.

Area = length x width

The result is always expressed in square units. If you measure in metres, the area is in square metres (m²). If you measure in centimetres, the area is in square centimetres (cm²), and so on. This is because you are multiplying a length by a length, which gives a two-dimensional unit.

Perimeter of a Rectangle

The perimeter is the total length of all four sides. Since a rectangle has two pairs of equal sides, the formula is:

Perimeter = 2 x (length + width)

For example, a 10 m x 5 m rectangle has a perimeter of 2 x (10 + 5) = 30 m. The perimeter is useful when fencing a garden, laying a border, or framing a picture.

Diagonal of a Rectangle

The diagonal connects two opposite corners of the rectangle, splitting it into two right-angled triangles. You can find the diagonal length using Pythagoras's theorem, where the diagonal is the hypotenuse:

Diagonal = sqrt(length² + width²)

For a 10 m x 5 m rectangle: Diagonal = sqrt(100 + 25) = sqrt(125) = 11.18 m. Knowing the diagonal is useful in construction and joinery to check that a frame is perfectly square (if both diagonals are equal, the corners are true right angles).

Common Applications

Application	What you need	Formula used
Painting a wall	Surface area to cover	Area = L x W
Buying flooring or carpet	Floor area in m²	Area = L x W
Fencing a garden bed	Total border length	Perimeter = 2(L + W)
Checking a frame is square	Corner-to-corner distance	Diagonal = sqrt(L² + W²)
Laying irrigation pipe	Total pipe around perimeter	Perimeter = 2(L + W)

Unit Conversions for Area

When working with area, be careful with unit conversions. Because area is a two-dimensional measurement, conversion factors are squared. For instance, 1 metre = 100 centimetres, so 1 m² = 100 x 100 = 10,000 cm². Common conversions include:

1 m² = 10,000 cm²
1 m² = 1,000,000 mm²
1 m² = 10.764 ft²
1 m² = 1,550 in²
1 hectare = 10,000 m²

This calculator shows the area in multiple units automatically once you enter your dimensions.

Related Calculators

Maths and Stats Calculators: full hub of geometry and maths tools.
Area Calculator: area for a range of common shapes.
Area of a Circle Calculator: circular area using pi x radius squared.
Area of a Triangle Calculator: half base times height, or using coordinates.
Perimeter Calculator: perimeter for rectangles and other polygons.

Method: Standard Euclidean geometry. Area = l x w; Perimeter = 2(l + w); Diagonal = sqrt(l² + w²) by Pythagoras's theorem. These relationships hold for all rectangles and are taught in the New Zealand Mathematics and Statistics curriculum from Year 6 onwards (NZ Curriculum, Ministry of Education).

Results are calculated to up to 4 significant figures. For very large or very small dimensions, verify with your own measurements. This tool is suitable for everyday estimation; consult a qualified professional for building consents, engineering drawings, or legal boundary purposes.