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MasterMath

Rectangle Diagonal Calculator

The diagonal of a rectangle, which is the hypotenuse of the right triangle its two sides make, plus the angle it forms with the base.

Diagonal

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Diagonal—
Area—
Perimeter—
Angle with the base—
Ratio—

How this was worked out

    The formula

    d = √(base² + height²)

    Where it comes from

    A diagonal splits a rectangle into two identical right triangles whose legs are the sides. So the diagonal is simply the hypotenuse, and Pythagoras gives it directly.

    How to work it out by hand

    1. Square the base
    2. Square the height and add it
    3. Take the square root
    4. For the angle, take the arctangent of height over base

    What is worth knowing

    Screen sizes are the everyday application and the everyday confusion: a television is sold by its diagonal, which says nothing about its shape. A 55-inch 16:9 screen and a 55-inch 4:3 screen have the same diagonal and very different areas — the 4:3 one is noticeably larger. That is why switching from a 4:3 to a 16:9 set of the same nominal size felt like a downgrade to many people, and they were right. The ratio matters as much as the number.

    Frequently asked questions

    How do you find the diagonal of a rectangle?

    Square both sides, add them, and take the square root. It is Pythagoras applied to the two sides.

    Why do screens use the diagonal?

    Convention from the television industry. It is a single number, but it hides the aspect ratio, which determines the actual area.

    Do both diagonals have the same length?

    In a rectangle, yes. In a general parallelogram they do not.

    What is the angle with the base?

    The arctangent of the height divided by the base. For a square it is always 45°.