Television and monitor sizes are sold by one number, the diagonal, but nobody hangs a diagonal on a wall. You need the width and the height, and those are not printed on the box in a way that is easy to compare. A 55-inch television sounds like a fixed size, but a 55-inch 16:9 screen and a 55-inch 21:9 screen have very different widths and heights. This calculator turns the diagonal and the aspect ratio into real width and height, in inches and centimetres, so you can measure before you buy.
The maths is again Pythagoras. The diagonal, the width, and the height form a right-angled triangle, and the aspect ratio tells you the proportions of the width and the height. For a 16:9 screen, the width is sixteen parts and the height is nine parts of the same unit, and the diagonal is the square root of sixteen squared plus nine squared, which is about 18.36 parts. Divide the diagonal by 18.36 and multiply by sixteen for the width, and by nine for the height, and you have the real dimensions.
Here is a worked example. A 55-inch 16:9 television has a width of 55 times 16 divided by 18.36, which is 47.9 inches, or about 121.7 centimetres, and a height of 55 times 9 divided by 18.36, which is 27.0 inches, or about 68.5 centimetres. The same 55-inch diagonal in 21:9 gives a width of about 50.9 inches but a height of only 21.8 inches, which is much wider and much shorter. That difference decides whether the screen fits above a fireplace, under a shelf, or between two windows.
The most common mistake is forgetting the frame. The diagonal is measured across the screen itself, the glowing part, not the plastic or metal around it. Modern screens have thin bezels, often under a centimetre, but a television with a soundbar built into the bottom frame can be several centimetres taller than the screen height alone. Always add the frame and the stand to the numbers this tool gives you, and check the full product dimensions in the specifications before you drill holes or order a wall mount.
Aspect ratio also changes how much picture you actually see. A 21:9 ultrawide monitor shows more of a spreadsheet or a video timeline side by side, which is why editors and programmers like them, but films made for 16:9 will show black bars on the sides or be cropped. A 16:10 laptop screen is slightly taller than a 16:9 screen of the same diagonal, which gives more room for documents and web pages. The right ratio depends on what you do most, not on which number sounds biggest.
Wall mounting deserves special care, because the mount and the cables add depth and the viewing height matters as much as the size. The centre of the screen should sit roughly at eye level when you are seated, which is lower than most people mount their televisions. A screen that is too high causes neck strain over a long film, no matter how good the picture is. Measure the width and height with this tool, mark the outline on the wall with tape, and sit in your usual seat before you commit to a position.
Use this calculator for every screen purchase, from a small monitor to a large television, and write the width and height on your shopping list next to the diagonal. Measure the space it must fit, add room for the frame, the stand, and the cables, and leave a little air around the screen for cooling. A screen that fits its space looks better and lasts longer than a screen that was squeezed in, and five minutes with this tool is what stands between the two.
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