Rectangle Formulas (Area, Perimeter, Diagonal)

A rectangle is a quadrilateral with four right angles and opposite sides equal. Its area is length times width, A = l·w; its perimeter is P = 2(l + w); and its diagonal is d = √(l² + w²) by the Pythagorean theorem.

Rectangle formulas

Area: $A = l \cdot w$
Perimeter: $P = 2(l + w)$
Diagonal: $d = \sqrt{l^2 + w^2}$

where l = length, w = width, A = area, P = perimeter, d = diagonal

Area

A = l \cdot w

Worked example

A rectangle 8 long and 5 wide has area 40 square units.

A = l\cdot w = 8\cdot 5 = 40

Perimeter

P = 2(l + w)

Worked example

Its perimeter is 26 units.

P = 2(l + w) = 2(8 + 5) = 26

Diagonal

d = \sqrt{l^2 + w^2}

Interactive rectangle explorer

Drag a slider (or type a value, or use the arrow keys) and watch the diagram, the results, and the full step-by-step substitution update live.

Length l

Width w

Area A 40units²

Perimeter P 26units

Diagonal d 9.43units

Step-by-step substitution

A = l · w = 8 · 5 = 40
P = 2(l + w) = 2(8 + 5) = 26
d = √(l² + w²) = √(64 + 25) = 9.43

Classroom use: rectangle formulas

Who it's for: Grades 3–8 · Elementary and middle-school students learning area and perimeter of rectangles, including students who need the length/width distinction reinforced.

Learning objectives

After using this page, students will be able to:

Compute area and perimeter of a rectangle from its length and width.
Explain why two rectangles can share a perimeter but differ in area.
Solve for a missing dimension given the area and one side.

Suggested classroom activity

Fix the perimeter at 24 and have students find every whole-number rectangle that fits, using the explorer to check each one. They discover the square maximises area — a genuine result reached by experiment rather than assertion.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`3.MD.C.7`	Relate area to multiplication and addition.
`3.MD.D.8`	Solve real-world problems involving perimeters of polygons.
`6.G.A.1`	Find the area of triangles, special quadrilaterals, and polygons by composing or decomposing shapes.
`6.G.A.3`	Draw polygons in the coordinate plane; use coordinates to find side lengths.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Related & next steps

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Frequently asked questions

What is the area formula for a rectangle?

The area of a rectangle is A = l·w, length multiplied by width. A rectangle 10 by 4 has area 10 × 4 = 40 square units.

How do you find the perimeter of a rectangle?

Add length and width and double the result: P = 2(l + w). For a 10 × 4 rectangle, P = 2(10 + 4) = 28 units.

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