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Diagonal Calculator

Find the diagonal of a rectangle, square or 3D box, or get the width and height of a screen from its diagonal and aspect ratio.

About this tool

Calculate diagonals four ways: a rectangle from its length and width, a square from its side, a 3D box from its three edges, or the real width and height of a screen from its diagonal and aspect ratio. Everything is computed in your browser.

The diagonals use the Pythagorean theorem: a rectangle is √(l² + w²), a square is s·√2, and a box's space diagonal is √(l² + w² + h²). For screen sizing with an aspect ratio w:h (for example 16:9), the scale factor is diagonal / √(w² + h²); the width is w × scale, the height is h × scale, and the display area is width × height.

The screen mode is ideal for TVs and monitors: enter a 50 inch diagonal at 16:9 to see it measures about 43.6 by 24.5 inches. The other modes also report area, perimeter, volume or surface area where they apply.

Frequently asked questions

How is a rectangle's diagonal calculated?
By the Pythagorean theorem: diagonal = √(length² + width²). A square is the special case s·√2 where length equals width.
What is the space diagonal of a box?
The longest straight line inside a rectangular box, corner to opposite corner, equal to √(length² + width² + height²).
How does the screen-size mode work?
It scales the aspect ratio to the given diagonal: scale = diagonal / √(w² + h²), then width = w × scale and height = h × scale, so a 16:9 50-inch TV is about 43.6 by 24.5 inches.
Do the units matter?
No. Diagonals are unit-agnostic — inches in gives inches out. Just keep every measurement in the same unit within one calculation.

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