Diagonal of a Rectangle
Calculate the diagonal length of a rectangle using the Pythagorean theorem.
Used in construction, screens, and layout design.
The Formula
d = √(l² + w²)
The diagonal of a rectangle is the straight line connecting opposite corners. It forms a right triangle with the length and width, so the Pythagorean theorem applies.
Variables
| Symbol | Meaning |
|---|---|
| d | Length of the diagonal |
| l | Length of the rectangle |
| w | Width of the rectangle |
Example 1
A TV screen is 48 inches wide and 27 inches tall. What is the diagonal?
d = √(48² + 27²) = √(2304 + 729)
d = √3033
d ≈ 55.1 inches (a "55-inch" TV)
Example 2
A room is 5 m long and 4 m wide. What is the diagonal distance?
d = √(5² + 4²) = √(25 + 16) = √41
d ≈ 6.40 m
When to Use It
Use the diagonal formula when:
- Measuring TV, monitor, or phone screen sizes
- Checking if a rectangular space is square (diagonals should be equal)
- Calculating the longest item that fits in a rectangular box
- Laying out foundations and framing in construction