Quiz: Area of a Rectangle Calculator

Enter a rectangle's length and width to calculate its area, perimeter, and diagonal using A = length × width.

Quick Facts

Formula
A = length × width
Perimeter = 2 × (length + width); a square is just a rectangle where length = width.

Your Results

Calculated
Area
-
Length × width
Perimeter
-
2 × (length + width)
Diagonal
-
√(length² + width²)
Aspect ratio
-
Length : width

Ready

Enter a length and width, then press Calculate.

Formula and method for Area of a Rectangle

Area of a Rectangle:

A = length × width

A rectangle's area is the amount of flat surface it covers, found by multiplying two perpendicular side lengths. This calculator also derives the perimeter (the distance around the outside) and the diagonal (the straight-line distance between opposite corners), using the same length and width you enter.

How the calculation works

Area comes straight from A = length × width. Perimeter adds all four sides — two lengths and two widths — which simplifies to P = 2 × (length + width). The diagonal splits the rectangle into two right triangles, so the Pythagorean theorem gives d = √(length² + width²). Enter your measurements in one consistent unit — mixing feet and inches, or centimeters and meters, produces incorrect results. The unit selector above only relabels the output; it does not convert between units.

Common mistakes

  • Units: area is in square units (ft², m²), while perimeter and diagonal stay in linear units (ft, m). A rectangle 3 ft by 3 ft has an area of 9 ft², not 9 ft.
  • Area vs. perimeter: a 12 × 8 rectangle has an area of 96 (square units) but a perimeter of only 40 (linear units) — they are not interchangeable and rarely equal.
  • Diagonal vs. side length: the diagonal is always longer than either side; for a 12 × 8 rectangle it is about 14.42, not simply length + width or the larger side.

Real-world applications

  • Flooring, paint, carpet, and tiling projects use area to estimate material quantities (add 10–15% for waste/cuts)
  • Fencing, baseboards, and edging use perimeter for planning linear material
  • Furniture, screens, and door/window openings use the diagonal to check whether an item fits through a space
  • Land plots, room layouts, and construction drawings use all three together for planning and material estimates

Frequently Asked Questions

What is the formula for the area of a rectangle?
Area equals length times width: A = length × width. If a rectangle is 12 ft long and 8 ft wide, its area is 12 × 8 = 96 square feet. The result is always in square units, since you are multiplying two length measurements together.
How do you find the perimeter of a rectangle?
Perimeter is the total distance around the rectangle: P = 2 × (length + width). For a 12 × 8 rectangle, the perimeter is 2 × (12 + 8) = 40 units. Unlike area, perimeter stays in linear units (feet, meters, etc.), not square units.
How is a rectangle's diagonal calculated?
The diagonal connects two opposite corners and is found with the Pythagorean theorem: d = √(length² + width²). For a 12 × 8 rectangle, the diagonal is √(144 + 64) = √208 ≈ 14.42 units.
Is a square a rectangle?
Yes. A square is a special case of a rectangle where all four sides are equal (length = width). The same area, perimeter, and diagonal formulas apply — a square just has length and width set to the same value.

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