Screen Size Calculator — width, height & area from diagonal

How it works

Screens are sold by their diagonal measurement, but what usually matters — will it fit, how big is the picture — is the width and height. The diagonal is the hypotenuse of the rectangle, so by the Pythagorean theorem (MathWorld), for an aspect ratio of a:b:

Width = diagonal × a ÷ √(a² + b²)

Height = diagonal × b ÷ √(a² + b²)

Area = width × height

The aspect ratio is the shape of the screen — 16:9 for most TVs and monitors, 4:3 for older displays, and taller ratios like 19.5:9 for phones. Because two screens with the same diagonal but different ratios have different widths, heights and areas, the diagonal alone can be misleading: a wide 21:9 monitor and a 16:9 monitor of the same diagonal are not the same size picture. A key consequence is that, for a fixed diagonal, a squarer screen has more area than a wider one — the diagonal is "spent" more efficiently.

Worked example

A 55-inch TV with a 16:9 aspect ratio:

• √(16² + 9²) = √337 ≈ 18.358
• Width: 55 × 16 ÷ 18.358 ≈ 47.94 in
• Height: 55 × 9 ÷ 18.358 ≈ 26.96 in
• Area: 47.94 × 26.96 ≈ 1,293 sq in

As a clean check, a 100-inch 4:3 screen works out to exactly 80 × 60 inches — a 3-4-5 right triangle scaled up.

Frequently asked questions

How do I find a screen's width and height from its size?

The advertised size is the diagonal. For an a:b aspect ratio, width = diagonal × a ÷ √(a² + b²) and height = diagonal × b ÷ √(a² + b²). A 55-inch 16:9 screen is about 47.9 × 27.0 inches.

Why isn't a 55-inch screen 55 inches wide?

Because 55 inches is the diagonal, corner to corner. The width and height are always smaller, and how much smaller depends on the aspect ratio.

Do two screens with the same diagonal have the same area?

No. A squarer aspect ratio (like 4:3) gives more area than a wider one (like 21:9) for the same diagonal, because the diagonal is shared differently between width and height.

What aspect ratio should I use?

Use 16:9 for most modern TVs and monitors, 4:3 for older or some specialty displays, and the phone's listed ratio (often around 19.5:9 or 20:9) for smartphones. Enter whatever the device specifies.

How do I know if a TV will fit my space?

Compute its width and height here and compare to the opening in your cabinet or the wall space, allowing a little margin for the bezel and stand. The diagonal alone won't tell you if it fits.

Can I use this for phones and laptops too?

Yes. The math is the same for any rectangular screen — enter the diagonal and the device's aspect ratio to get its physical width, height and area.