The calculation
Pixels per inch is the diagonal in pixels divided by the diagonal in inches. The diagonal in pixels comes from Pythagoras: the square root of width squared plus height squared. Nothing else is involved, which is why the figure is exact rather than approximate.
A 27-inch panel at 2560 x 1440: 2560 squared is 6,553,600 and 1440 squared is 2,073,600, which sum to 8,627,200. The square root is 2937.21 pixels across the diagonal, and 2937.21 divided by 27 is 108.79 PPI. A 15.6-inch laptop at 1920 x 1080: the diagonal is 2202.91 pixels, divided by 15.6 gives 141.21 PPI. Rounded specs usually quote these as 109 and 141.
Dot pitch is the same information inverted — the centre-to-centre spacing of adjacent pixels, conventionally in millimetres, so 25.4 divided by the PPI. At 108.79 PPI that is 0.2335 mm. Monitor spec sheets from the CRT era quoted pitch instead of density and the habit survives in industrial displays.
Where the retina threshold comes from
20/20 vision resolves detail down to about one arcminute, a sixtieth of a degree. Two points closer together than that angle merge. At a viewing distance d, one arcminute covers d x tan(1/60°) of screen, so the density at which pixels stop being individually distinguishable is the reciprocal of that.
| Screen | Typical distance | Threshold density |
|---|---|---|
| Phone | 12 in | ~286 PPI |
| Laptop | 18 in | ~191 PPI |
| Desk monitor | 24 in | ~143 PPI |
| Living-room TV | 96 in | ~36 PPI |
This is why a phone needs 300 PPI and a 65-inch 4K television at 68 PPI is comfortably past the same standard from a sofa. It is also why the marketing term is meaningless without a distance attached: a 27-inch 4K monitor at 163 PPI clears the desk threshold, and a 43-inch 4K at 102 PPI does not.
Treat one arcminute as a floor, not a target. Vernier acuity — spotting that a line is not straight — beats it by a wide margin, plenty of people test better than 20/20, and text is the worst case because it is all high-contrast edges. Roughly 1.3 times the threshold is where the returns genuinely flatten.
Density, scaling and how much desktop you get
Windows and macOS both assume something in the region of 96 to 110 PPI for unscaled interface elements. That is why 24-inch 1080p at 92 PPI and 27-inch 1440p at 109 PPI are the two sizes people run at 100% without complaint.
Above that you scale, and scaling trades working area for sharpness. A 27-inch 4K at 163 PPI run at 150% gives you the desktop area of a 1440p screen with far crisper text. The catch is that 150% is not an integer factor: the compositor renders at a fractional multiple and resamples, and applications that do their own drawing — older Windows software especially — come out soft. 200% is an integer factor and is clean, which is the reason 5K 27-inch panels and high-DPI laptops pick densities that land there.
Where the number stops being the whole story
Diagonal is quoted for the active area, not the outside of the chassis, so it is comparable between models but not to a tape measure over the bezel. Ultrawides at 21:9 or 32:9 have less area than a 16:9 panel of the same diagonal even at identical density. Phone screens lose pixels to rounded corners and cutouts, so the nominal resolution slightly overstates what is drawn. And subpixel layout matters at the margin: a PenTile OLED with fewer red and blue subpixels than green resolves fine detail worse than an RGB-stripe LCD at the same PPI, which is why two phones with matching spec-sheet densities can differ visibly on small text.
Questions people ask
27-inch 4K or 32-inch 4K?
Same pixel count, different jobs. The 27 is 163 PPI and wants 150% scaling, which gives you a 1440p-sized desktop that looks noticeably sharper than an actual 1440p panel. The 32 is 138 PPI and works at 125%, which yields more usable area — around 3072 x 1728 logical — with text that is good rather than exceptional. From a normal 24-inch viewing distance both clear the resolvability threshold, so this is a question about how much desktop you want, not about sharpness.
Is PPI the same as DPI?
Not originally, though the terms have collapsed together in casual use. PPI counts display pixels per inch. DPI counts printer ink dots per inch, and a printer lays down several dots of different inks to make one perceived colour, so a 1200 DPI printer is not resolving 1200 distinct image points per inch. The other place DPI appears is as a metadata tag inside an image file, where it is a note about intended print size and changes nothing about the pixels. For anything on a screen, PPI is the term that means something.
How should I measure viewing distance?
Sit the way you actually sit and measure from your eyes to the centre of the screen in a straight line, not along the desk. Most people are further back than they assume — a typical desk monitor sits at 22 to 28 inches, a laptop at 16 to 20 because the keyboard pulls it closer, and a phone at 10 to 14. For a television, measure from the sofa rather than trusting the room dimensions.
Does higher density always mean a better display?
Past the threshold for your distance, it mostly means a bigger GPU load, more power drawn, and a scaling factor you have to configure. Contrast ratio, colour accuracy, refresh rate, panel uniformity and how the thing behaves in your room lighting all affect the experience more than another 40 PPI does once you are already above about 1.3 times the threshold. Density is easy to put on a box, which is why it ends up on the box.