Rectangle Calculator
Rectangle Formulas and Calculations
What is a Rectangle?
A rectangle is a quadrilateral with four right angles. It is one of the most common shapes in geometry and in everyday life. A rectangle has the following properties:
- All four angles are 90° (right angles)
- Opposite sides are parallel and equal in length
- Diagonals bisect each other (divide each other in half)
- Diagonals are equal in length
Rectangle Formulas
Area (A) = length × width
Perimeter (P) = 2 × (length + width)
Diagonal (d) = √(length² + width²)
How to Use This Calculator
- Enter the length of the rectangle.
- Enter the width of the rectangle.
- Select the unit of measurement.
- Click "Calculate" to see the results.
Special Types of Rectangles
Square
A square is a special type of rectangle where all sides are equal in length. For a square:
- Area = side² (where side is the length of any side)
- Perimeter = 4 × side
- Diagonal = side × √2
Golden Rectangle
A golden rectangle has a length-to-width ratio equal to the golden ratio (approximately 1.618:1). This rectangle is considered aesthetically pleasing and appears in art, architecture, and nature.
Applications of Rectangle Calculations
Practical Uses
- Construction and Architecture: Calculating flooring area, wall dimensions, material requirements.
- Interior Design: Planning room layouts, furniture placement, carpet and tile requirements.
- Engineering: Designing rectangular components, calculating material needs.
- Agriculture: Planning field layouts, calculating seed and fertilizer requirements.
- Everyday Life: Calculating paint needed for walls, fabric for curtains, or paper for wrapping.
Example Calculations
Example 1: A rectangular room measures 12 feet in length and 10 feet in width. What is its area, perimeter, and diagonal length?
Area = 12 × 10 = 120 square feet
Perimeter = 2 × (12 + 10) = 2 × 22 = 44 feet
Diagonal = √(12² + 10²) = √(144 + 100) = √244 ≈ 15.62 feet
Example 2: How much carpet is needed to cover a rectangular floor that measures 5 meters by 3 meters?
Area = 5 × 3 = 15 square meters of carpet
FAQ
What's the difference between a rectangle and a square?
A square is a special type of rectangle where all four sides are equal in length. All squares are rectangles, but not all rectangles are squares.
How do I find the area of a rectangle?
The area of a rectangle is calculated by multiplying its length by its width: Area = length × width.
How do I find the diagonal of a rectangle?
The diagonal of a rectangle can be calculated using the Pythagorean theorem: Diagonal = √(length² + width²).
Can this calculator be used for a square?
Yes, simply enter the same value for both length and width to calculate properties of a square.
Rectangle Dimension Table
| Length | Width | Area | Perimeter | Diagonal |
|---|---|---|---|---|
| 3 | 2 | 6 | 10 | 3.61 |
| 4 | 3 | 12 | 14 | 5.00 |
| 5 | 4 | 20 | 18 | 6.40 |
| 6 | 4 | 24 | 20 | 7.21 |
| 8 | 5 | 40 | 26 | 9.43 |
| 10 | 8 | 80 | 36 | 12.81 |