Diagonal of Rectangle Calculator

How to calculate the diagonal of a rectangle

The diagonal of a rectangle can be calculated using the Pythagorean theorem. Since the diagonal creates a right triangle with the width and height, we can use:

$$d = \sqrt{w^2 + h^2}$$

Where:

• d = diagonal length
• w = width
• h = height

Example

For a rectangle with width 16 and height 9:

$$\begin{aligned} d &= \sqrt{16^2 + 9^2} \\ d &= \sqrt{256 + 81} \\ d &= \sqrt{337} \\ d &\approx 18.36 \end{aligned}$$

Properties of rectangle diagonals

• A rectangle has two diagonals of equal length
• The diagonals bisect each other (cross at their midpoints)
• Each diagonal divides the rectangle into two congruent right triangles
• The diagonals are not perpendicular (unless it's a square)

Common applications

• TV and monitor sizes: Screen size is measured diagonally
• Construction: Checking if corners are square (3-4-5 rule)
• Packaging: Determining if items fit diagonally in boxes
• Sports fields: Measuring field dimensions

Related formulas

Property	Formula
Diagonal	d = √(w² + h²)
Area	A = w × h
Perimeter	P = 2(w + h)

Special case: square

For a square where w = h = s:

$$d = s\sqrt{2} \approx 1.414s$$