The diagonal is the only size a screen advertises — and the least useful one
Screens are sold by a single number, the diagonal, a convention inherited from round picture tubes. But nothing in your home is diagonal-shaped: a television must fit a stand's width, a monitor a desk's span, a phone a pocket, and all of those are governed by the width and height, which the diagonal conceals — because two screens with the same diagonal but different aspect ratios have different widths, different heights and noticeably different areas. This calculator recovers the real dimensions: enter the diagonal and the aspect ratio and it returns width and height in inches and centimetres, plus the viewing area. The default is the modern standard, a 55-inch 16:9 screen: 47.94 inches wide by 26.96 inches tall (about 121.8 × 68.5 cm), roughly 1,293 square inches of picture — the numbers you actually need before ordering the stand.
The geometry: one triangle, one division
The aspect ratio describes a unit rectangle — 16 units wide, 9 tall — whose own diagonal is √(16² + 9²) = √337 ≈ 18.36 units. Your screen is that rectangle scaled until its diagonal matches the advertised size, so each side scales by the same factor: width takes 16/18.36 of the diagonal (about 87.2% of it for 16:9) and height takes 9/18.36 (about 49.0%). Those two fractions are worth remembering as rules of thumb for any 16:9 screen: the width is a little under seven-eighths of the diagonal, the height a little under half. The step panel shows the division with your own numbers, and centimetres are just inches × 2.54, the exact definition.
Why the ratio matters more than the diagonal
Compare shapes at one diagonal and the advertisement number falls apart. A 55-inch screen in the old 4:3 ratio would be 44 inches wide and 33 tall — far less wide, much taller, and about 13% more area than the 16:9 version, because squarer shapes pack more area into the same diagonal. A 21:9 ultrawide at the same diagonal stretches to roughly 50.3 inches wide but only 21.5 tall, with less area still: wonderful for spreadsheets side by side and cinematic films, disappointing for ordinary television, which arrives pillarboxed with black bars consuming the extra width. Phones quote diagonals that include tall 19.5:9 or 20:9 ratios, so a “6.7-inch” phone is mostly height. Whenever two screens are compared — a TV upgrade, a monitor swap — compare widths and areas from this page, not diagonals: jumping from a 43-inch to a 55-inch 16:9 set grows the area by about 64%, which is the upgrade your eyes will actually report.
Worked example
Worked through for the default 55-inch 16:9: the ratio's diagonal is √337 ≈ 18.358. Width = 55 × 16 ÷ 18.358 = 47.94 in (121.76 cm); height = 55 × 9 ÷ 18.358 = 26.96 in (68.49 cm); area ≈ 1,293 sq in. The common sizes at 16:9, for reference: 32 in ≈ 27.89 × 15.69 in, 43 in ≈ 37.48 × 21.08 in, 65 in ≈ 56.65 × 31.87 in, 75 in ≈ 65.37 × 36.77 in.
How to use this calculator
- Enter the advertised diagonal in inches.
- Choose the aspect ratio — 16:9 unless you know it is something else.
- Read the true width and height in the headline and table, in inches and centimetres.
- Add your device's bezel and stand measurements before deciding it fits a space.
- Compare upgrades by area in the stats, not by diagonal.
Viewing distance, briefly
Width converts to a sensible viewing distance with one more rule of thumb: for mixed television and film viewing, sit roughly 1.2 to 1.6 times the diagonal away — about 5.5 to 7.5 feet for the 55-inch default — closer for cinema-first rooms (around 1× the diagonal fills the recommended field of view) and farther for mostly-news viewing. The honest constraint is usually the room, not the rule: measure the wall and the seating, take the width from this page to check the fit against furniture, and let the distance land where the room puts it. A screen whose width you know can be mocked up on the wall with painter's tape in two minutes, which settles more arguments than any chart — tape the 47.94 × 26.96 outline before the 55-inch set arrives, not after.