Screen Size Calculator

Background.

A screen is sold by one number — 43, 55, 65, 77 inches — and that number is a diagonal, not a width. On its own it tells you almost nothing about whether the television will fit the alcove, whether the monitor will leave room for a second one, or how much bigger the upgrade really is. This calculator does the geometry that turns the marketing number into the two measurements that actually matter: how wide the panel is and how tall it is, in inches and centimetres, along with the picture area and the exact aspect ratio.

The conversion is pure Pythagoras. A screen with sides in the ratio a to b has a width of a·k and a height of b·k for some common scale factor k, and the diagonal closes the right-angled triangle formed by those two sides. Setting D² = (a·k)² + (b·k)² and solving gives k = D ÷ √(a² + b²), after which the width and height fall straight out. For the near-universal 16:9 shape, √(16² + 9²) = √337 ≈ 18.3576, so a 55-inch panel works out at 47.94 inches wide and 26.96 inches tall — a full seven inches narrower than most people guess when they hear "55 inches".

That 16:9 shape is not an arbitrary industry habit. Recommendation ITU-R BT.709, the parameter set behind essentially all HDTV production and international programme exchange, specifies an aspect ratio of 16:9 with 1 920 samples per active line, 1 080 active lines per picture, and a pixel aspect ratio of 1:1 — square pixels. Recommendation ITU-R BT.2020 carries the same 16:9 shape forward to the 3 840 × 2 160 and 7 680 × 4 320 ultra-high-definition formats. The older 4:3 shape, still found on legacy monitors and broadcast archives, is documented alongside 16:9 in Recommendation ITU-R BT.601. Because all of these formats use square pixels, the pixel ratio and the physical ratio are the same number, which is what makes a simple geometric calculation legitimate.

The area output deserves a moment of attention, because it is the figure that exposes how misleading diagonals can be. Screen area is width times height — which is precisely how Commission Regulation (EU) 2019/2013 defines the screen area of an electronic display for energy-label purposes. Rearranged, area = D²·ab ÷ (a² + b²), so for a fixed diagonal the area depends on the shape as well as the size. A 34-inch 21:9 ultrawide and a 34-inch 16:9 monitor share a diagonal but not a picture area: the wider panel is flatter, so it loses height faster than it gains width. Comparing two screens by diagonal alone quietly compares two different quantities.

The centimetre outputs are exact rather than approximate. The inch has been defined since 1 July 1959 as exactly 25.4 millimetres, a value NIST publishes as a definition rather than a measurement, so the conversion introduces no error of its own. Everything here is computed in arbitrary-precision decimal arithmetic and rounded only at the final display step.

The second mode runs the calculation backwards. If you have a tape measure and an actual panel — a second-hand monitor with no model number, a screen already on the wall, a projector image you want to characterise — enter the measured width and height and the calculator returns the diagonal it would be advertised at, the ratio reduced to lowest terms by the Euclidean algorithm, and the same area figures. Measure the lit area of the panel only: manufacturers quote the viewable diagonal, so including the bezel will inflate your answer by an inch or more.

What is screen size calculator?

Screen size is the length of the diagonal across the viewable area of a display, measured from one corner of the lit panel to the opposite corner and quoted in inches in North America and in centimetres in most of the rest of the world. It deliberately excludes the bezel, the frame and the stand, which is why a screen measured across its outer casing always reads larger than its advertised size.

A diagonal on its own is an incomplete description, because two screens with the same diagonal can have very different widths, heights and picture areas depending on their aspect ratio. Width and height are recovered from the diagonal by treating the screen as a right-angled triangle: the two sides are in the known ratio, the diagonal is the hypotenuse, and Pythagoras' theorem fixes the scale. The picture area — the quantity that actually corresponds to how much image you see — is then the product of that width and height, matching the regulatory definition of screen area used on EU energy labels.

How to use this calculator.

1. 01Choose whether you know the advertised diagonal (the usual case) or you have measured a physical panel.
2. 02Enter the diagonal in inches — the figure on the box, which refers to the viewable panel and not the outer bezel.
3. 03Enter the aspect ratio as two numbers: 16 and 9 for almost every modern TV and monitor, 16 and 10 for many productivity monitors, 21 and 9 for an ultrawide, 4 and 3 for a legacy display.
4. 04Read the width and height in inches and centimetres — these are the numbers to compare against your alcove, wall recess, desk depth or AV unit.
5. 05Check the picture area if you are comparing two screens of different shapes; equal diagonals do not mean equal area.
6. 06To go the other way, switch to the measured mode and enter the width and height of the lit area; the calculator returns the diagonal the screen would be sold as, plus its aspect ratio in lowest terms.

The formula.

Treat the screen as a rectangle whose width and height are in a known ratio a : b. Both sides therefore share a single unknown scale factor k, giving W = a·k and H = b·k. The diagonal is the hypotenuse of the right-angled triangle formed by those two sides, so by Pythagoras' theorem D² = W² + H² = (a·k)² + (b·k)² = k²(a² + b²). Solving for the scale factor gives k = D ÷ √(a² + b²), and the width and height follow immediately as a·k and b·k.

Running that on the default 16:9 shape: a² + b² = 256 + 81 = 337, and √337 = 18.35755975. For a 55-inch diagonal, k = 55 ÷ 18.35755975 = 2.99604091. The width is 16 × 2.99604091 = 47.93665456 inches and the height is 9 × 2.99604091 = 26.96436819 inches. Squaring and adding those two returns 3 025, which is 55² exactly — the check that the geometry closed correctly.

The area formula is worth writing out in full because it explains a counter-intuitive result. Substituting the width and height gives Area = a·b·k² = D²·ab ÷ (a² + b²). The diagonal enters squared, but so does the shape term ab ÷ (a² + b²), which peaks for a square panel and shrinks as the rectangle gets longer and thinner. For 16:9 that term is 144/337 = 0.4273; for 21:9 it is 189/522 = 0.3621. A 34-inch 21:9 screen therefore has roughly 15 per cent less picture area than a 34-inch 16:9 screen would, despite the identical advertised size.

The reverse direction needs no ratio input at all. Given a measured width and height, the diagonal is simply √(W² + H²), and the aspect ratio is the pair W : H reduced to lowest terms by dividing both by their greatest common divisor — found with the Euclidean algorithm, the same repeated-remainder procedure used to simplify an ordinary fraction. A measured 3 440 × 1 440 ultrawide reduces to 43 : 18, which is why that panel is marketed loosely as "21:9" even though it is not exactly that ratio.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Recommendation ITU-R BT.709-6 (06/2015), Parameter values for the HDTV standards for production and international programme exchange — §2.1 aspect ratio 16:9, §2.2 1 920 samples per active line, §2.4 1 080 active lines, §2.5 pixel aspect ratio 1:1 (square pixels). International Telecommunication Union.
2. [2]Recommendation ITU-R BT.601-7 (03/2011), Studio encoding parameters of digital television for standard 4:3 and wide-screen 16:9 aspect ratios. International Telecommunication Union.
3. [3]Recommendation ITU-R BT.2020-2 (10/2015), Parameter values for ultra-high definition television systems for production and international programme exchange — pixel counts 3 840 × 2 160 and 7 680 × 4 320, aspect ratio 16:9, pixel aspect ratio 1:1 (square pixels). International Telecommunication Union.
4. [4]Commission Regulation (EU) 2019/2013 of 11 March 2019 supplementing Regulation (EU) 2017/1369 with regard to energy labelling of electronic displays — Article 2 definition of 'screen area' as viewable image width multiplied by viewable image height. Official Journal of the European Union.
5. [5]National Institute of Standards and Technology, Office of Weights and Measures — SI Units: Length. The inch, derived from the international yard effective 1 July 1959, is exactly equivalent to 25.4 mm.