Rectangle Calculator: area, perimeter and diagonal

A rectangle is a quadrilateral with four right angles and equal opposite sides. This calculator computes the area, perimeter and diagonal from the length and width.

Rectangle formulas

For a rectangle with length l and width w:

• Area: A = l × w
• Perimeter: P = 2 × (l + w)
• Diagonal: d = √(l² + w²)

The diagonal is computed using the Pythagorean theorem, as it divides the rectangle into two congruent right triangles.

Example 1: rectangle with integer dimensions

Problem: A rectangle has length l = 8 cm and width w = 5 cm.

1. Area:
   • A = 8 × 5 = 40 cm².
2. Perimeter:
   • P = 2 × (8 + 5) = 2 × 13 = 26 cm.
3. Diagonal:
   • d = √(8² + 5²) = √(64 + 25) = √89 ≈ 9.43 cm.

Answer: A = 40 cm², P = 26 cm, d ≈ 9.43 cm.

Example 2: rectangle with decimal measurements

Problem: A rectangular room measures l = 4.5 m and w = 3.2 m.

1. Area:
   • A = 4.5 × 3.2 = 14.4 m².
2. Perimeter:
   • P = 2 × (4.5 + 3.2) = 2 × 7.7 = 15.4 m.
3. Diagonal:
   • d = √(4.5² + 3.2²) = √(20.25 + 10.24) = √30.49 ≈ 5.52 m.

Answer: A = 14.4 m², P = 15.4 m, d ≈ 5.52 m.

Häufige Anwendungsfälle

• Computing areas of rooms, plots and rectangular surfaces.
• Estimating materials for flooring, paint and coverings.
• Determining perimeter for fences, frames and borders.
• Computing the diagonal of screens, monitors and TVs.
• Solving basic geometry problems in school mathematics.
• Planning furniture layout and interior spaces.

Common mistakes when working with rectangles

• Confusing length with width when applying formulas for other shapes.
• Forgetting to multiply by 2 in the perimeter formula.
• Using the sum of sides instead of the Pythagorean theorem for the diagonal.
• Mixing units, such as length in meters and width in centimeters.

Profi-Tipp

If you know the area and one side, you can find the other side by dividing: w = A / l. If you know the perimeter and one side: w = P/2 − l. These inverse relationships are useful when you do not have both dimensions.