Area of a Rectangle Calculator
Calculate the area, perimeter, and diagonal of a rectangle. Find missing sides from known area. Convert between metric and imperial area units.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Area = Length x Width | Perimeter = 2(L + W) | Diagonal = sqrt(L² + W²)
The area of a rectangle is the product of its length and width. The perimeter is twice the sum of the two sides. The diagonal, found using the Pythagorean theorem, connects opposite corners. These three measurements fully characterize a rectangle's key geometric properties.
Worked Examples
Example 1: Room Floor Area
Problem:Calculate the area, perimeter, and diagonal of a room that is 4.5 meters long and 3.2 meters wide.
Solution:Area = 4.5 x 3.2 = 14.40 m²\nPerimeter = 2 x (4.5 + 3.2) = 2 x 7.7 = 15.40 m\nDiagonal = sqrt(4.5² + 3.2²) = sqrt(20.25 + 10.24) = sqrt(30.49) = 5.522 m\nAspect ratio = 4.5/3.2 = 1.406
Result:Area = 14.40 m² | Perimeter = 15.40 m | Diagonal = 5.522 m
Example 2: Finding a Missing Dimension
Problem:A rectangular garden has an area of 200 square feet and one side is 16 feet. Find the other side.
Solution:Area = Length x Width\n200 = 16 x Width\nWidth = 200 / 16 = 12.5 feet\nPerimeter = 2 x (16 + 12.5) = 57 feet\nDiagonal = sqrt(16² + 12.5²) = sqrt(256 + 156.25) = sqrt(412.25) = 20.304 feet
Result:Other side = 12.5 ft | Perimeter = 57 ft | Diagonal = 20.304 ft
Frequently Asked Questions
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. This formula works because a rectangle can be divided into unit squares, and the total number of unit squares equals the product of the two side lengths. For example, a rectangle that is 5 meters long and 3 meters wide contains 15 square meters (5 x 3 = 15 m²). The area is always expressed in square units (square meters, square feet, square centimeters, etc.), which represent the two-dimensional space enclosed by the rectangle. This is one of the most fundamental formulas in geometry and is used extensively in construction, real estate, interior design, agriculture, and engineering.
How do you find a missing side of a rectangle when you know the area?
If you know the area of a rectangle and one side, you can find the other side by dividing the area by the known side: Unknown Side = Area / Known Side. This is derived directly from rearranging the area formula (Area = Length x Width). For example, if a rectangular room has an area of 120 square feet and one wall is 10 feet long, the other dimension is 120 / 10 = 12 feet. This calculation is particularly useful in real-world scenarios such as determining how wide a plot of land is when you know its total acreage and one boundary length, or figuring out the length of material needed when the total coverage area and width are specified.
What is the difference between area and perimeter of a rectangle?
Area and perimeter measure fundamentally different properties of a rectangle. Area measures the total two-dimensional space inside the rectangle (Length x Width, in square units), answering questions like 'how much carpet do I need?' or 'how large is this field?' Perimeter measures the total distance around the outside edge (2 x Length + 2 x Width, in linear units), answering questions like 'how much fencing do I need?' or 'how long is the border?' Two rectangles can have the same perimeter but very different areas — for example, a 1x9 rectangle and a 5x5 square both have a perimeter of 20, but areas of 9 and 25 respectively. The shape that maximizes area for a given perimeter is always a square.
How do you calculate the diagonal of a rectangle?
The diagonal of a rectangle is calculated using the Pythagorean theorem: Diagonal = sqrt(Length² + Width²). The diagonal divides the rectangle into two right triangles, where the length and width are the two legs and the diagonal is the hypotenuse. For a rectangle that is 6 meters by 8 meters, the diagonal is sqrt(36 + 64) = sqrt(100) = 10 meters. This forms the well-known 3-4-5 Pythagorean triple (scaled by 2). Knowing the diagonal is practically important for construction workers who use the '3-4-5 rule' to verify that corners are perfectly square — if a rectangle's measured diagonal matches the calculated value, the corners are truly 90 degrees.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy