Area of a Rectangle Calculator

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.

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:

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:

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

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.