Rectangle Calculator
Find any rectangle measurement — area, perimeter, or diagonal — from any two known values such as length and width, area and a side, or perimeter and a side. Ideal for home improvement, flooring, and geometry homework.
About this calculator
A rectangle has four right angles with opposite sides equal. Its area is A = l × w, where l is length and w is width. The perimeter is P = 2(l + w), giving the total distance around the shape. The diagonal d connects opposite corners and is found using the Pythagorean theorem: d = √(l² + w²). This calculator is flexible — if you know the area and one side, it derives the missing side via w = A / l. If you know the perimeter and one side, it uses w = (P / 2) − l. All four properties are interrelated, so any two values are enough to compute the rest.
How to use
Suppose you know the length is 8 units and the width is 5 units, and you want the diagonal. Select 'Length & Width' as your known values, enter 8 for the first value and 5 for the second. Choose 'Diagonal' as what to calculate. The formula gives d = √(8² + 5²) = √(64 + 25) = √89 ≈ 9.43 units. To find the area instead, switch the output to 'Area': A = 8 × 5 = 40 square units.
Frequently asked questions
How do I find the diagonal of a rectangle if I only know the area and one side?
First, derive the missing side by dividing the area by the known side: w = A / l. Once you have both sides, apply the Pythagorean theorem: d = √(l² + w²). For example, if A = 40 and l = 8, then w = 5, and d = √(64 + 25) ≈ 9.43 units. This calculator performs all those steps automatically when you select 'Area & Length' as your known values.
What is the difference between perimeter and area of a rectangle?
Area measures the two-dimensional space enclosed by the rectangle, calculated as A = l × w and expressed in square units. Perimeter measures the total length of the boundary, calculated as P = 2(l + w) and expressed in linear units. A room that is 4 m × 6 m has an area of 24 m² (useful for flooring) and a perimeter of 20 m (useful for skirting boards). Understanding both is essential for most construction and design tasks.
When would I use perimeter and a known side to find a rectangle's dimensions?
This scenario arises when you have a fixed total length of material — like fencing or framing — and one dimension is already set. For example, if you have 20 m of fence and one side must be 6 m, the calculator uses w = (P / 2) − l = (20 / 2) − 6 = 4 m. This is common in garden design, picture framing, and room planning where one constraint is fixed by walls or materials.