# Diagonal of Rectangle Calculator

Calculate the diagonal of a rectangle from width and height using the Pythagorean theorem. Also shows area, perimeter, and diagonal angle. Free calculator.

## What this calculates

Calculate the diagonal length of any rectangle by entering its width and height. This calculator uses the Pythagorean theorem and also computes the area, perimeter, diagonal angle, and aspect ratio.

## Inputs

- **Width** — min 0 — The horizontal side of the rectangle.
- **Height** — min 0 — The vertical side of the rectangle.

## Outputs

- **Diagonal Length** — The length of the diagonal: sqrt(width^2 + height^2).
- **Area** — The area of the rectangle (width x height).
- **Perimeter** — The total length of all four sides.
- **Diagonal Angle** — formatted as text — The angle the diagonal makes with the width side, in degrees.
- **Aspect Ratio** — formatted as text — The ratio of width to height.

## Details

The diagonal of a rectangle connects two opposite corners. Since it divides the rectangle into two right triangles, the Pythagorean theorem gives us the length.

**Diagonal Formula:**

d = sqrt(width^2 + height^2)

**Example:**

A rectangle with width 3 and height 4 has diagonal = sqrt(9 + 16) = sqrt(25) = 5. This is the classic 3-4-5 right triangle.

**Diagonal Angle:**

The diagonal makes an angle with the width side: angle = arctan(height / width). For the 3-4-5 rectangle, the angle is arctan(4/3) = 53.13 degrees.

**Common Uses:**

- **TV and monitor sizes** are measured by the diagonal. A "55-inch TV" has a 55-inch diagonal.
- **Construction:** Finding the diagonal ensures right angles (the 3-4-5 rule is used on job sites).
- **Shipping:** The diagonal determines whether a long object fits inside a rectangular box.
- **Screen resolution:** The diagonal, combined with pixel count, determines pixel density (PPI).

## Frequently Asked Questions

**Q: How do I calculate the diagonal of a rectangle?**

A: Use the formula d = sqrt(width^2 + height^2). This comes directly from the Pythagorean theorem, since the diagonal is the hypotenuse of a right triangle formed by the width and height. For a rectangle that is 8 cm wide and 6 cm tall, the diagonal = sqrt(64 + 36) = sqrt(100) = 10 cm.

**Q: How is TV screen size related to the diagonal?**

A: TV and monitor sizes are measured by the diagonal, not the width or height. A 55-inch TV means the diagonal from one corner to the opposite corner is 55 inches. The actual width and height depend on the aspect ratio (typically 16:9). For a 55-inch 16:9 TV, the width is about 47.9 inches and the height is about 27.0 inches.

**Q: How do I find the width if I know the diagonal and height?**

A: Rearrange the formula: width = sqrt(diagonal^2 - height^2). For example, if the diagonal is 10 and the height is 6: width = sqrt(100 - 36) = sqrt(64) = 8. This works because the same Pythagorean relationship applies in reverse.

**Q: Are the two diagonals of a rectangle equal?**

A: Yes. Every rectangle has two diagonals and they are always equal in length. They also bisect each other (cross at their midpoints). This is a defining property of rectangles. In a square (a special rectangle), the diagonals are also perpendicular.

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Source: https://vastcalc.com/calculators/math/diagonal-of-rectangle
Category: Math
Last updated: 2026-04-08