PPI (pixels per inch) equals the square root of horizontal pixels squared plus vertical pixels squared, divided by the diagonal screen size in inches — PPI = √(w² + h²) ÷ d. The math comes from the Pythagorean theorem: the screen's pixel rectangle has a diagonal that runs corner to corner through every pixel in the array, and once you know how long that diagonal is in pixels, dividing by the diagonal in inches tells you how many pixels fit into each linear inch. For a 1920×1080 panel measured at 24 inches, the pixel diagonal comes out to roughly 2,202.91 pixels, and 2,202.91 ÷ 24 is about 91.79 pixels per inch. That figure is the single cleanest way to compare the real sharpness of two displays, because the marketing labels "1080p" or "4K" only describe how many pixels the panel contains, not how tightly those pixels are packed. A 6.7-inch phone carrying the same resolution as a 55-inch TV squeezes those pixels into a far smaller physical area and looks noticeably crisper for it. Entering the three numbers into the PPI Calculator runs the whole calculation in your browser, with no signup and nothing uploaded — the diagonal-pixel step, the PPI result, dot pitch, pixels per centimetre, aspect ratio and megapixel count all refresh as you type.
What PPI Actually Measures (and Why It Differs From DPI)
PPI stands for pixels per inch, the count of individual pixels packed into one linear inch of a display's surface. The same figure is also called pixel density, and it captures the one thing a resolution label does not: how crowded those pixels are physically. A 55-inch TV labelled 4K and a 24-inch monitor labelled 4K both contain about 8.3 million pixels, but on the smaller monitor each pixel sits much closer to its neighbours, so text and edges look smoother at the same viewing distance.
You will also see the closely related term DPI (dots per inch). The two are often used interchangeably, but the technical split is clean: PPI refers to pixel density on a screen, while DPI refers to the density of ink dots that a printer lays down on paper. When you are comparing monitors, laptops, phones or tablets, PPI is the correct term. When you are working out print resolution, DPI is the one that matters.
The PPI Formula in Plain Terms
The full formula, written out:
PPI = √(width² + height²) ÷ diagonal size in inches
The width and height are the horizontal and vertical pixel counts of the panel — for example 1920 and 1080. The diagonal is the screen's measured corner-to-corner size in inches — for example 24. Squaring and adding the two pixel counts produces the square of the diagonal pixel count, and the square root turns that back into the actual length. Dividing by the physical diagonal in inches then converts "pixels along the diagonal" into "pixels per inch".
Here is the calculation worked through one step at a time for a common 24-inch 1080p monitor:
- Width² = 1,920 × 1,920 = 3,686,400
- Height² = 1,080 × 1,080 = 1,166,400
- Sum of squares = 3,686,400 + 1,166,400 = 4,852,800
- Square root of the sum ≈ 2,202.91 pixels along the diagonal
- PPI = 2,202.91 ÷ 24 ≈ 91.79 PPI
That is the same figure the PPI Calculator reports the instant those three inputs are typed in, and the same three-step pattern works for any panel: the diagonal-pixel step is the intermediate result, and PPI is the final answer in pixels per inch.
How to Calculate PPI for Any Display
To produce the same number without doing the arithmetic by hand, follow these steps inside the calculator.
- Enter the horizontal resolution of your screen in pixels — for example 1920 for a Full HD panel, 2560 for a 1440p panel, or 3840 for a 4K panel.
- Enter the vertical resolution in pixels — for example 1080 to match a 16:9 panel, 1440 for a 1440p panel, or 2160 for a 4K panel.
- Enter the diagonal screen size in inches — for example 24 — or tap a preset such as the 1080p 24-inch button if your panel matches one.
- Read the PPI result alongside the dot pitch in millimetres, pixels per centimetre and aspect ratio, all of which update as you type. The diagonal pixel count and total megapixels update at the same time, which makes it easy to confirm the panel type at a glance.
Typing the values is fast, and the calculator does the Pythagorean step in the background, so there is no need to square 1,920 and 1,080 on paper. Comparing two displays is as simple as changing one number and watching the result move.
Typical PPI Ranges by Device
Different devices are designed for different viewing distances, and that is why PPI varies so widely across categories. The table below groups the typical densities cited for common device types, using ranges rather than per-model computations so the figures read as a guide, not a verdict on a specific device.
| Device type | Typical PPI range | Typical viewing distance | Why the range sits where it does |
|---|---|---|---|
| Modern flagship smartphone | Around 400-500 PPI | Held close, roughly 10-15 inches from the eyes | Phones sit closest to the eye, so density needs to be very high to hide individual pixels. |
| Mid-range smartphone | Around 300-400 PPI | Same close distance | Still past the typical "Retina" threshold for phone use, sharp for everyday reading and video. |
| Laptop screen | Around 120-220 PPI | Lap or desk, roughly 16-24 inches | Sits farther than a phone, so 2K and "Retina-class" densities look clean without extreme GPU demand. |
| Desktop monitor (24-32 inches) | Around 90-140 PPI | Arm's length or further, roughly 20-36 inches | Most common 24-inch 1080p monitors land near 90 PPI, 27-inch 1440p near 109 PPI, 32-inch 4K near 138 PPI. |
| Living-room TV (55-85 inches) | Often well under 100 PPI | Several feet away | PPI is low on purpose, because the eye cannot resolve fine pixels at TV viewing distance anyway. |
The same exact PPI value can look pixelated on a phone held six inches from your face and perfectly fine on a TV across the room. When two devices in the same category have different sizes, comparing them by PPI is more informative than comparing them by the resolution label alone. For a specific screen's number, type its resolution and diagonal into the PPI Calculator rather than reading off a typical range.
Beyond PPI: Dot Pitch, PPcm and Aspect Ratio
The calculator also reports three figures that sit alongside PPI and often make a screen easier to interpret.
- Dot pitch — the distance, in millimetres, between the centres of two neighbouring pixels. Smaller dot pitch means finer detail. It comes from the formula 25.4 ÷ PPI, so a 91.79 PPI panel has a dot pitch of about 0.277 mm.
- PPcm (pixels per centimetre) — the metric counterpart to PPI, equal to PPI ÷ 2.54. Useful if you measure or document screens in centimetres rather than inches.
- Aspect ratio — the simplified width-to-height ratio such as 16:9, 16:10, 21:9 (ultrawide), 4:3 or 5:4. The reduced ratio makes unusual panels easy to recognise at a glance.
Dot pitch is the figure most cited by display and signage professionals because the gap between pixels is what the eye actually perceives. A 91.79 PPI screen's 0.277 mm pitch reads as smooth for desktop use; the same physical pitch on a phone held close to the eyes would look noticeably grainy.
Apple popularised the marketing term Retina for screens where individual pixels are too small to resolve at a normal viewing distance. The threshold is not one fixed number: on iPhones it works out to roughly 300+ PPI, on MacBook displays around 220 PPI, and on the iMac about 218 PPI. Two screens carrying the same Retina label can therefore have very different pixel counts behind the scenes.
Higher PPI generally means a sharper image, but only up to the point your eye can resolve at your viewing distance. Pushing density further costs GPU power and requires operating-system UI scaling to keep text and icons at a usable physical size. For most desktop monitors the practical sweet spot is around 90-140 PPI, for laptops 120-220, and for phones 300 and up. Numbers above those ranges add little visible sharpness and demand more from the rest of the system.