SamCalculator

Rectangle Area Calculator

Calculate rectangle area, perimeter, diagonal length, aspect ratio, and area conversions instantly across metric and imperial units.

Choose a shape

Rectangle inputs

A = l × w
m
m

Master area formula library

Rectangle

A = l × w

Length times width.

Square

A = s²

A rectangle with equal sides.

Triangle

A = ½ × b × h

Half the base times the height.

Triangle (Heron)

A = √[s(s−a)(s−b)(s−c)]

From three side lengths only.

Trapezoid

A = ½(b₁ + b₂) × h

Average of the parallel bases × height.

Circle

A = π × r²

Pi times the radius squared.

Sector

A = ½ × r² × θ

Radians for θ.

Ellipse

A = π × a × b

Semi-major × semi-minor × π.

Parallelogram

A = b × h

Base times perpendicular height.

Rhombus

A = ½ × d₁ × d₂

Half the product of the diagonals.

Kite

A = ½ × d₁ × d₂

Same as the rhombus diagonal rule.

Regular polygon

A = ½ × n × s × a

n sides of length s, apothem a.

Polygon

A = ½ |Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|

Shoelace / Surveyor's formula.

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What Is the Rectangle Area Formula?

A rectangle is a four-sided figure with four right angles. Opposite sides are equal in length, the diagonals are equal and bisect each other, and the area follows the simplest of all area rules: length times width. Once you know two adjacent sides, every other property — perimeter, diagonal, aspect ratio, area in any unit — falls out of straightforward algebra.

The formula used on this page is A = l × w. The calculator applies it instantly, returns full unit conversions, and shows every substitution in the step-by-step panel.

How the Calculation Works

The rectangle area formula A = l × w is so foundational that it underpins almost every other 2D shape: a parallelogram is a sheared rectangle (same area), a triangle is half a rectangle (A = ½bh), and the Shoelace formula for arbitrary polygons reduces to repeated rectangle subtractions. The perimeter is P = 2(l + w) — twice the half-perimeter. The diagonal length comes from the Pythagorean theorem applied to the two adjacent sides: d² = l² + w². Aspect ratio is just l ÷ w, a unit-free measure of how stretched the rectangle is.

6 Ways to Use This Rectangle Calculator

1

Plan a room or floor area

Multiply length by width to size flooring, paint, tile, or carpet. The calculator converts the result to square feet and square metres at the same time.

2

Estimate land or lot size

For a rectangular plot, length × width gives the area in your input unit. The conversion panel then translates to acres and hectares for property comparisons.

3

Find a diagonal length

The diagonal d = √(l² + w²) tells you the longest straight line that fits inside the rectangle — useful for camera sensors, TV screens, and shipping boxes.

4

Check an aspect ratio

Aspect ratio is length ÷ width. A standard A-series sheet has a ratio close to √2; widescreen video is 16 : 9 ≈ 1.78.

5

Convert between unit systems

Enter dimensions in metres and instantly read the area in square feet, or vice-versa, without juggling conversion factors.

6

Validate engineering layouts

Confirm parts, panels, or PCBs match a target footprint, perimeter, or diagonal envelope before procurement.

Best Practices

  • Mixing metric and imperial. Length and width must use the same unit. Converting one side to feet without converting the other will produce an area off by a factor of about ten.
  • Slanted versus perpendicular sides. Rectangle area assumes right angles. If your shape is a parallelogram (slanted), use the parallelogram calculator and the perpendicular height rather than the slant length.
  • Confusing perimeter and area. Two shapes with the same perimeter can have very different areas. A square has the largest area among all rectangles with a given perimeter.
  • Squaring the diagonal accidentally. Diagonal is √(l² + w²), not l² + w². Squaring then forgetting the square root overstates the diagonal.

Why Rectangle Area Matters

Floor plans and room sizing

Real-estate listings, paint coverage, flooring orders, and rug shopping all rely on rectangular area.

Land plots and parcels

Surveyed lots are often rectangular. Length × width gives the area in your unit; conversion to acres or hectares is the standard real-estate vocabulary.

Print and display sizing

Paper sizes, signage, billboards, monitors, and TVs are specified by their length, width, and (diagonal × aspect ratio).

PCB and panel layout

Electronic boards, photovoltaic panels, and architectural cladding panels are dimensioned as rectangles for cutting, packaging, and shipping.

Common Mistakes

  • Using slant rather than perpendicular height. Only relevant when generalising to parallelograms — the rectangle's sides are already perpendicular.
  • Forgetting to square the unit on output. Length × width yields units squared (m × m = m²). The displayed unit suffix carries the square automatically.
  • Reporting area as a length. Area is a 2D measure. Calling a 200 m² plot '200 metres' is dimensionally wrong.

Core Formula

Formula

A = l × w

Area is always returned in your input unit squared. The conversion panel translates the result into mm², cm², m², ha, km², in², ft², yd², acres, and mi² so you can compare across unit systems.

Methodology & Accuracy

Every calculation runs entirely in your browser using JavaScript's full double-precision arithmetic (about 15–17 significant digits internally). The displayed result is rounded to four significant figures by default; numbers outside the 0.0001 to 999,999,999 range switch automatically to scientific notation. The rectangle formula used here is the standard Euclidean-geometry identity, sourced from the same textbooks used in secondary-school and university geometry courses.

Frequently Asked Questions

Area equals length times width: A = l × w. Make sure both values use the same unit; the result will be in that unit squared (for example, metres × metres gives m²).

Use the Pythagorean theorem: d = √(l² + w²). The diagonal divides the rectangle into two right-angled triangles, so the diagonal is the hypotenuse.

Aspect ratio is length ÷ width. A 16:9 widescreen panel has an aspect ratio of about 1.78; a perfect square has a ratio of 1.

No — convert both length and width to the same unit before multiplying. The area panel then converts the result into every common metric and imperial unit automatically.

Because a square is a special case of a rectangle where l = w. The formula collapses to A = s², where s is the common side length.

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