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Screen PPI Calculator

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A resolution on its own tells you almost nothing. A 3840 × 2160 panel is either extraordinarily sharp or thoroughly ordinary depending entirely on whether it is a 15-inch laptop or a 65-inch television, and specification sheets quote the pixel count while saying nothing about the density. Enter a resolution and a diagonal and this gives the pixels per inch, the actual physical size of the panel, and the distance beyond which adding more pixels stops making any difference to what you can see.

px
px
in

As advertised — screens are sold by the diagonal

Common screens:

How to use the screen ppi calculator

  1. 1Enter the horizontal and vertical resolution in pixels.
  2. 2Enter the screen diagonal in inches — the figure it was advertised as.
  3. 3Press Calculate, or pick one of the common screens to compare against.
  4. 4Read the pixel density, the panel's real width and height, and the dot pitch.
  5. 5The viewing distance figure is the closest you can sit before individual pixels become resolvable.

Examples

A common desktop monitor

Input
2560 × 1440 at 27 inches
Result
108.8 PPI, panel 23.5 × 13.2 inches

The density most desktop interfaces were designed around, and the reason 27-inch 1440p is such a common choice.

The same resolution, smaller panel

Input
1920 × 1080 at 13.3 inches
Result
165.6 PPI

Half again the density of a 24-inch 1080p monitor, which is why the same interface needs scaling on a laptop.

A television

Input
3840 × 2160 at 55 inches
Result
80.1 PPI — lower than any monitor here

Perfectly sharp from a sofa, because what matters is the angle a pixel subtends at your eye rather than its size.

About the screen ppi calculator

Getting the physical size back out of a specification

A specification gives a pixel count and a diagonal, and both of the numbers people actually want — how wide is it, how sharp is it — have to be recovered from those. The diagonal in pixels comes from Pythagoras, and dividing it by the diagonal in inches gives the density. Once the density is known, the physical width is the pixel width divided by it, and the same for the height.

That recovery is more useful than it sounds, because a diagonal alone does not determine a size. A 34-inch ultrawide at 21:9 is 31.4 inches across and 13.5 tall; a 34-inch 16:9 panel would be 29.6 by 16.7. Same diagonal, very different desk footprint and very different amount of vertical space, which is the thing people actually notice after buying one.

It also settles comparisons between formats. A 16:9 panel and a 4:3 panel of the same diagonal differ by about 20% in area, with the 4:3 panel larger — which is why the switch to widescreen made monitors feel smaller at the same nominal size, and why the industry moved up a size class shortly afterwards.

The viewing distance figure, and what it is for

Human visual acuity is conventionally taken as one arcminute — a sixtieth of a degree — which is the angular size of the gap in the letters on the 20/20 line of an eye chart. A pixel subtends that angle at a distance determined by its physical size, and beyond that distance the eye cannot separate it from its neighbour. That is the number this page reports, and it is the honest version of the marketing term.

Two things follow. The first is that density requirements scale with proximity: a phone at 30 cm, a monitor at 60 cm and a television at 3 m need roughly ten, five and one times the pixels per inch to be equally sharp. The second is that resolution arguments are meaningless without a distance attached. 4K on a 32-inch monitor at desk distance is a genuine improvement; 8K on the same monitor is not, because the pixels were already indistinguishable.

The one-arcminute figure is a population average and better-than-average eyes do somewhat better, particularly at high-contrast edges like text on a white background — which is why text always looks sharper at higher densities even when photographs stop improving. It is a reasonable threshold rather than a hard limit, and it is worth treating as the point where returns start diminishing rather than the point where they stop.

Frequently asked questions

Is a higher PPI always better?
Only up to the point where your eye stops resolving the difference, and that point depends on how far away you sit. Beyond roughly one arcminute of visual angle — the standard definition of normal acuity — additional pixels land closer together than the eye can separate, and they cost power, bandwidth and money for nothing visible. A phone held at 30 cm genuinely benefits from 400 PPI; a television watched from three metres does not benefit from 100.
What is dot pitch, and how does it relate to PPI?
Dot pitch is the distance between the centres of neighbouring pixels, usually in millimetres, and it is simply the reciprocal of pixel density. A 100 PPI display has a dot pitch of 0.254 mm. The two say exactly the same thing, and which one gets quoted is largely a matter of era and industry: monitor specifications used dot pitch for decades before phones made PPI the familiar figure.
Why is PPI measured along the diagonal?
Because that is where the arithmetic is cleanest and because screens are sold by their diagonal. The number of pixels along the diagonal comes straight from Pythagoras on the width and height, and dividing by the advertised diagonal gives the density directly. It also happens to be the same figure you would get measuring horizontally or vertically, since pixels on essentially every modern display are square.
Does PPI decide how large text appears?
No — the operating system's scaling setting does. On a high-density display, running the interface at 100% would make everything tiny, so the system draws it at 150% or 200% and uses the extra pixels for sharpness rather than for showing more content. That is why a 4K laptop and a 1080p laptop of the same size can show identical amounts of text with one looking far crisper. Apparent size is a setting; sharpness is the panel.
How does this compare with DPI for printing?
The arithmetic is the same and the context is not. A screen's density is fixed by its hardware and viewed from a metre or so; a print's resolution is chosen at the moment of printing and held at arm's length, which is why 300 DPI is the usual print target while 100 PPI is unremarkable on a monitor. The paper size converter on this site handles the printing side, where the question is how many pixels a given physical sheet needs.

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