Area of a Rectangle Calculator

A = length × width.

Result

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How to use this calculator

Enter length and width in any unit.
Read area, perimeter, and diagonal.

About this calculator

The most basic formula in geometry: length × width. The diagonal is computed via the Pythagorean theorem. This formula extends to any 2D space — a rectangle on a map, a wall to be painted, a piece of fabric.

How it works — the formula

A = length × width
Diagonal d = √(length² + width²)  (Pythagoras)

The area of a rectangle is the product of its two adjacent sides. This is the simplest case of the integral that defines area: an axis-aligned rectangle of length ℓ and width w has area exactly ℓw. The diagonal follows from Pythagoras' theorem, since the diagonal is the hypotenuse of a right triangle whose legs are the rectangle's sides.

Sources: NIST SP 811 — Quantities and units (area) · Wolfram MathWorld — Rectangle · BOMA International — BOMA Standards (real-world floor area methods of measurement)

Worked examples

Example 1

Room dimensions

Inputs:: 12 ft × 14 ft
Output:: A = 168 ft²; diagonal = √(144 + 196) ≈ 18.44 ft

Example 2

Display size

Inputs:: 52.3 in × 29.4 in
Output:: A ≈ 1,538 in²; diagonal ≈ 60 in (typical 60-inch TV)

Example 3

Square as a special case

Inputs:: 8 m × 8 m
Output:: A = 64 m²; diagonal = 8√2 ≈ 11.31 m

Limitations

Formula applies only to rectangles (4 right angles). For parallelograms, multiply base × perpendicular height; for trapezoids, use the (b₁+b₂)·h/2 formula.
Real "rooms" rarely have exactly perpendicular walls; surveyors use the laser-distance + diagonals method to detect non-square rooms.
BOMA / IPMS standards distinguish gross, net, and rentable floor area — definitions matter for leases.
For very large land plots the Earth's curvature matters; geodesic area formulas replace the flat rectangle.

Area is exact arithmetic; real measurements inherit tape-measure tolerance (±1/16 in for handheld, ±1 mm for laser).