What is a rectangle?
A rectangle is a quadrilateral with four right angles. Its opposite sides have equal lengths, so two adjacent dimensions are enough to describe the whole shape.
Rectangle formulas
For a rectangle with length l and width w, the three core measurements are area, perimeter, and diagonal. These formulas agree with the standard relationships used by CalculatorSoup, Omni Calculator, and Inch Calculator.
Multiply the two perpendicular side lengths.
Add all four sides; opposite sides are equal.
Apply the Pythagorean theorem to half of the rectangle.
Worked rectangle examples
Worked examples make the formulas easier to recognize. The classic 3–4–5 rectangle is especially useful because its diagonal is an integer.
Example 1 · 3 × 4 rectangle
Example 2 · 12 × 5 rectangle
How to find a missing side
If you know the area and one side, divide the area by the known side. If you know the perimeter and one side, subtract the two known copies of that side and divide by two. If you know the diagonal and one side, use the Pythagorean theorem.
Given area A and length l
w = A ÷ l. Example: 60 cm² ÷ 12 cm = 5 cm.
Given perimeter P and length l
w = P/2 − l. Example: 34/2 − 12 = 5 cm.
Given diagonal d and length l
w = √(d² − l²). Example: √(13² − 12²) = 5 cm.
Given area A and width w
l = A ÷ w. The same area relationship works in either direction.
Important properties of a rectangle
| Property | Relationship | Why it matters |
|---|---|---|
| Opposite sides | l = l and w = w | Only two adjacent side lengths are needed. |
| Angles | 4 × 90° | Each diagonal creates right triangles. |
| Diagonals | d₁ = d₂ | Both diagonals have the same length and bisect each other. |
| Area | A = l × w | Measures the two-dimensional space inside. |
| Perimeter | P = 2(l + w) | Measures the total boundary length. |
Where rectangles are used
Rectangle calculations appear in construction, flooring, painting, packaging, screens, tables, gardens, rooms, signs, and many design problems. Inch Calculator specifically highlights flooring and tiling, painting, construction, agriculture and landscaping, and design as practical applications.
Rooms & flooring
Multiply room length by width to estimate floor area and material quantities.
Screens & paper
Rectangular dimensions describe screens, posters, sheets, labels and many packages.
Construction
Perimeter can represent edging or trim, while area represents a surface to cover.
Is a square a rectangle?
Yes. A square is a special rectangle in which the length and width are equal. If l = w = s, the rectangle formulas become A = s², P = 4s, and d = s√2.
How to check a rectangle calculation
Unit check
Lengths use units such as cm or m; area uses square units such as cm² or m²; perimeter and diagonal return length units.
Scale check
If length doubles while width stays fixed, area doubles. Perimeter increases by 2 × the added length.
Triangle check
The diagonal must be longer than either side and satisfy d² = l² + w².
Boundary check
Perimeter should always equal the sum of all four sides: l + w + l + w.
Rectangle calculator FAQ
Area is A = l × w. Multiply the length by the width, using the same unit for both measurements.
Perimeter is P = 2(l + w), which is the sum of the four sides.
Use d = √(l² + w²). The diagonal acts as the hypotenuse of a right triangle formed by the two side lengths.
Yes. Enter any two compatible known properties. For example, w = A/l, w = P/2 − l, or w = √(d² − l²), depending on the information you know.
Any consistent length unit works. If the sides are in meters, area is in square meters and perimeter and diagonal are in meters. If the two sides use different units, convert them to the same unit first. citeturn0view0
Yes. A square has four right angles and equal opposite sides, so it satisfies the rectangle definition; it simply adds the condition that all four sides are equal.