Area of a Rectangle Calculator

A = length × width.

Inputs

Result

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General calculation reads

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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).

Frequently asked

Does the order of length and width matter?+
No — multiplication is commutative.
Why is the formula different from a parallelogram?+
It's not — a rectangle is a parallelogram with right angles. The general formula b × h applies.
How do I split a rectangle into squares?+
Find the GCD of length and width — that's the size of the largest square that tiles the rectangle exactly.
What units?+
Whatever you input — feet × feet = ft², meters × meters = m².
Can length and width be the same?+
Yes — that's a square (a special rectangle).

Related calculators

Area of a Square Calculator
A = s² where s is the side length.
Area of a Parallelogram Calculator
A = base × height (perpendicular height).
Area of a Trapezoid Calculator
A = ½ × (parallel side a + parallel side b) × height.
Rectangle Perimeter Calculator
P = 2(l + w). Length plus width, doubled.
Rectangular Prism Volume
V = l × w × h. Box / cuboid volume.
Pythagorean Theorem Calculator
a² + b² = c². Solve for hypotenuse or missing leg of a right triangle.

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