PPI Calculator

PPI (pixels per inch) tells you how tightly packed the pixels on a screen are. It comes from the resolution and the diagonal size, nothing else. A 1920 x 1080 monitor measured at 24 inches diagonally works out to 91.8 PPI, which means each pixel is about 0.277 mm across. Higher PPI equals a finer, smoother picture at the same viewing distance.

Three neighboring tools handle the questions this page does not. The Aspect Ratio Calculator works out the shape of a frame and solves a missing width or height, the Ratio Calculator handles abstract proportions that have nothing to do with screens, and the Unit Converter moves between inches, centimeters and millimeters when your screen is specified metrically. Use this page when you want the density itself: how sharp a given resolution will look on a given piece of glass.

How pixel density is calculated

Screen sizes are quoted as a diagonal, so the pixel grid has to be measured along the same diagonal before the two can be compared. That is a plain application of the Pythagorean theorem:

where W and H are the horizontal and vertical pixel counts and D is the advertised diagonal in inches. The numerator is the length of the screen diagonal expressed in pixels; dividing by the same diagonal in inches leaves pixels per inch. If your screen is specified in centimeters, divide by 2.54 first, or just flip the unit control in the calculator above.

Two follow-on figures fall straight out of the same result. Dot pitch, the physical distance from the center of one pixel to the center of the next, is the reciprocal expressed in millimeters:

And the physical width and height come from splitting the diagonal in the same proportion as the pixel counts:

A fully worked example: 1080p on a 24-inch monitor

Take the most ordinary desktop setup there is, a 1920 x 1080 panel advertised as 24 inches. Step one, the diagonal in pixels:

√(1920² + 1080²) = √(3,686,400 + 1,166,400) = √4,852,800 = 2,202.91 pixels.

Step two, divide by the physical diagonal: 2,202.91 ÷ 24 = 91.8 PPI. Step three, the dot pitch: 25.4 ÷ 91.79 = 0.2767 mm, a little over a quarter of a millimeter per pixel. Step four, the physical dimensions: the width is 24 × 1920 ÷ 2,202.91 = 20.92 inches (53.1 cm) and the height is 24 × 1080 ÷ 2,202.91 = 11.77 inches (29.9 cm), giving a viewing area of about 246 square inches. The panel carries 1920 × 1080 = 2,073,600 pixels, or 2.07 megapixels, in an aspect ratio that reduces to 16:9 because the greatest common divisor of 1920 and 1080 is 120.

One more number is worth having: at 91.8 PPI a single pixel shrinks to one arcminute of vision at roughly 37 inches. Most people sit closer than that at a desk, which is exactly why individual pixels are faintly visible on a 24-inch 1080p monitor if you look for them.

PPI of common resolutions at common screen sizes

The table below applies the formula to five widespread resolutions across six typical diagonals. Read down a column to see density collapse as the screen grows; read across a row to see it climb as pixels are added.

Two entries in that grid are worth memorizing because they define the mainstream desktop experience: 24-inch 1080p at 91.8 PPI and 27-inch 1440p at 108.8 PPI. Notice also that 32-inch 1440p lands on exactly the same 91.8 PPI as 24-inch 1080p, so the two feel identically sharp even though one shows far more content. Conversely, a 27-inch 4K panel at 163.2 PPI is precisely double the 27-inch 1080p figure of 81.6, since 3840 x 2160 is 1920 x 1080 doubled in both directions.

Dot pitch and pixels per centimeter

Monitor spec sheets, especially European ones, often quote dot pitch in millimeters instead of PPI. The two carry identical information. This table converts between them, and adds the metric density figure for good measure.

A useful anchor: at exactly 100 PPI the dot pitch is 0.254 mm, because 25.4 mm is one inch. Every other row in the table is that number scaled up or down.

Physical size of a 16:9 screen by diagonal

Because the diagonal alone does not tell you how much desk or wall a screen will occupy, this table converts 16:9 diagonals into actual width and height, and adds the density that 1080p and 4K deliver at each size.

A 16:9 screen is always 87.2% of its diagonal in width and 49.0% in height, so the arithmetic scales linearly: a 65-inch television is 56.65 inches wide, just over four and a half feet.

How to use this PPI calculator

Four inputs, and the result updates as you type. Work through them in order:

1. Pick a resolution preset if your screen matches one of the six standards, from 720p through 5K. That fills in the pixel width and height for you.
2. Or type the pixel counts directly into the width and height fields. Any whole numbers work, including odd panel sizes such as 1366 x 768, 3024 x 1964 or 2732 x 2048.
3. Choose the measurement unit. Inches is the default because US screens are advertised that way; switching to centimeters converts the number you already entered rather than discarding it.
4. Enter the diagonal size or tap one of the quick presets (13.3, 15.6, 24, 27, 32 or 55 inches). Use the advertised size, or measure corner to corner across the lit area for a precise figure.

The pink result card gives the headline PPI plus dot pitch, pixels per centimeter, total megapixels and the simplified aspect ratio. Below it you get the physical dimensions in both unit systems, the viewing area, and the distance at which the pixel grid disappears. The final table repeats your resolution across ten diagonals so you can see immediately whether the same panel would be better at a different size.

Who this calculator is for

• Monitor shoppers deciding between a 27-inch 1440p and a 32-inch 4K panel, where the spec sheets do not print density.
• Designers and photographers who need to know how many real inches a 1000-pixel element will occupy on a client's screen.
• Developers reasoning about CSS pixels, device pixel ratio and which images to ship at 2x.
• Home theater builders checking whether a 65-inch 4K set is sharp enough from the couch.
• Anyone comparing phones or tablets where marketing quotes resolution and diagonal but never the density that actually determines sharpness.
• Students and teachers working through a practical Pythagorean theorem problem with real numbers.

A second worked example: a 34-inch ultrawide

Ultrawide monitors break the 16:9 habit, so the arithmetic is worth seeing once. A 3440 x 1440 panel measured at 34 inches has a pixel diagonal of √(3440² + 1440²) = √(11,833,600 + 2,073,600) = 3,729.24 pixels. Dividing by 34 gives 109.7 PPI, with a dot pitch of 0.2316 mm.

The physical dimensions follow: the width is 34 × 3440 ÷ 3,729.24 = 31.36 inches and the height is 34 × 1440 ÷ 3,729.24 = 13.13 inches. So a 34-inch ultrawide is more than two and a half feet wide but only about 13 inches tall, roughly the same height as a 27-inch 16:9 monitor. The panel carries 4,953,600 pixels, or 4.95 megapixels, and the aspect ratio reduces to 43:18 because the greatest common divisor of 3440 and 1440 is 80, which is why "21:9" is a marketing label rather than an exact description.

The practical takeaway is that 109.7 PPI puts this ultrawide within a hair of a 27-inch 1440p monitor at 108.8 PPI. Text will look essentially identical on both; you are buying width, not sharpness.

How much density do you actually need?

Density on its own means nothing. What matters is the angle a pixel subtends at your eye, and that depends on how far away you sit. The widely used threshold is one arcminute per pixel, which for 20/20 vision is roughly the limit of what the eye can resolve. Turned into a formula, the density needed at a given distance is about 3,438 divided by the distance in inches:

Compare those targets with the density table above and the picture clears up fast. A 24-inch 1080p monitor at 91.8 PPI falls well short of the 143 PPI wanted at desk distance, so its pixels are faintly visible. A 65-inch 4K television at 67.8 PPI comfortably beats the 35.8 PPI needed from an eight-foot couch, which is why 8K sets deliver so little visible benefit in an ordinary living room.

Key terms explained

• PPI (pixels per inch): how many pixels fit into one linear inch of screen. The single number this calculator produces.
• Dot pitch: the center-to-center spacing between neighboring pixels, quoted in millimeters. Lower is sharper.
• Resolution: the raw pixel count, such as 2560 x 1440. It says nothing about sharpness until you pair it with a physical size.
• Aspect ratio: the shape of the frame, found by dividing width and height by their greatest common divisor. 1920 x 1080 reduces to 16:9.
• Device pixel ratio: the number of physical pixels a browser draws per CSS pixel. A 2x display packs four physical pixels into the area of one logical pixel.
• Subpixel: the red, green and blue elements that make up one pixel. Layouts differ between panels, which is why two screens at the same PPI can render text slightly differently.
• Arcminute: one sixtieth of a degree of visual angle, the common yardstick for the resolving limit of healthy human vision.

What changes the result the most

• Resolution: the dominant lever. Going from 1080p to 4K on the same panel doubles PPI exactly, because both dimensions double.
• Diagonal size: inversely proportional. The same pixels on a 32-inch screen instead of a 24-inch one drop density by a quarter, from 91.8 to 68.8 PPI.
• Aspect ratio: a secondary but real effect. Stretching the same pixel count into a wider frame lengthens the diagonal in pixels and nudges density up.
• Measurement accuracy: a half-inch error on a 13-inch laptop shifts the answer by about 4%, while the same error on a 55-inch television barely moves it.
• Rounded advertised sizes: a set sold as 55 inches may measure 54.6, and a "15.6-inch" laptop is genuinely 15.6, so use the real diagonal when precision matters.

PPI versus DPI: why the terms get mixed up

Search traffic for "DPI calculator screen" is enormous, and almost all of it wants PPI. DPI means dots per inch and belongs to printing: it counts the ink droplets a printer sprays onto paper, and a single image pixel is normally reproduced by several overlapping dots of different colors. PPI counts self-illuminating pixels on a display, one per addressable point. The arithmetic in this calculator is the same either way, since both are a count divided by a length, but the physical meaning differs. A photo prepared at 300 PPI for print and a phone panel at 300 PPI have nothing in common except the number. When you are talking about screens, PPI is the accurate word, and any tool that calls it DPI is using shorthand.

Density, scaling and how big things actually look

A high PPI does not automatically make text smaller, because operating systems scale the interface to compensate. On a 27-inch 4K monitor at 163.2 PPI, running at 100% scaling would make menu text roughly half the height it is on a 27-inch 1080p screen, which is uncomfortable for most people. Set scaling to 200% instead and every interface element occupies the same physical size as it did at 81.6 PPI, but is drawn with four times as many pixels, so edges and letterforms are far smoother. That is the whole point of a high-density display: the same layout, rendered more finely.

Fractional scaling, typically 125% or 150%, sits between those two states and is where high-density panels can disappoint. Because interface elements no longer map onto whole numbers of physical pixels, some applications resample their output and lines can look slightly soft. If you plan to run fractional scaling, aim for a density where 150% is comfortable, roughly 130 to 160 PPI, rather than assuming more pixels are always better. Web developers meet the same idea as the device pixel ratio: a 2x screen expects images at twice the nominal dimensions, and shipping a 1x asset to a 400 PPI phone is what makes a logo look blurry.

Practical tips

• Match density to distance, not to a spec sheet. Work out how far your eyes sit from the screen, read the PPI you need from the distance table, and buy to that target.
• Compare candidates at equal density before comparing price. A 32-inch 1440p and a 24-inch 1080p panel are both 91.8 PPI, so the larger one only buys you physical size and desk presence.
• Check whether your target density scales cleanly. Densities near 110 PPI work well at 100%, and densities near 160 to 220 PPI work well at 200%.
• Measure the panel if the listing is vague. Corner to corner across the lit area, ignoring the bezel, gives the number this formula expects.
• Remember that content resolution matters too. A 4K panel showing a 1080p video is limited by the video, not by the glass.
• Use the dot pitch figure when comparing older monitors, since many specification sheets from that era list pitch instead of density.

Limitations and assumptions

The formula is exact geometry, but a few real-world caveats apply:

• It assumes square pixels, which is true of virtually every modern display but not of some legacy broadcast formats.
• It assumes a flat panel. On a strongly curved monitor the straight-line diagonal is marginally shorter than the measured surface diagonal, so the true density is a fraction higher than reported.
• It ignores subpixel arrangement. Two panels at the same PPI can render text with different apparent sharpness depending on whether they use an RGB stripe or a diamond layout.
• It uses the advertised diagonal you type in. If the manufacturer rounds, the answer inherits that rounding.
• The arcminute threshold is a convention based on 20/20 vision. Sharper eyes resolve finer detail, and contrast, motion and viewing angle all shift what you actually notice.
• Density says nothing about brightness, contrast, color accuracy or refresh rate, which often matter more to how good a screen looks.

How it compares to related calculators

This page answers "how sharp is this screen?" If your question is a different one, a sister tool fits better:

• To find the shape of a frame or solve a missing width or height, use the Aspect Ratio Calculator.
• To reduce or compare any two quantities that are not screen dimensions, use the Ratio Calculator.
• To convert a diagonal between inches, centimeters and millimeters, use the Unit Converter.
• To turn the physical width and height into a surface area, use the Area Calculator.
• To work in feet for a wall-mounted television, use the Square Footage Calculator.

Sources

• The density formula is the Pythagorean theorem applied to the pixel grid, and the aspect ratio reduction uses Euclid's algorithm for the greatest common divisor. Both are elementary geometry and arithmetic, so no external source is needed or cited.
• The inch-to-millimeter and inch-to-centimeter conversions use the international inch defined as exactly 25.4 mm, the definition maintained by the National Institute of Standards and Technology (nist.gov/pml/owm).
• Resolution figures (1280 x 720, 1366 x 768, 1920 x 1080, 2560 x 1440, 3440 x 1440, 3840 x 2160, 5120 x 2880) are the pixel counts of the formats themselves. Every PPI, dot pitch, width, height and area on this page is computed from those counts and the stated diagonal, not quoted from a manufacturer or a third party.
• The one-arcminute visual acuity threshold used for the "pixels become invisible" distance is the conventional definition of 20/20 vision, in which a healthy eye resolves detail subtending one minute of arc. It is a convention, not a measurement of any particular person.