PPI Calculator

What pixels per inch measures

Pixels per inch is the number of pixels that fit along one inch of a screen. You cannot read it off the box, because the box lists resolution and diagonal size as separate numbers. The conversion is one square root and one division: take the width and height in pixels, find the diagonal in pixels with the Pythagorean theorem, then divide by the diagonal in inches.

That is the whole formula: PPI = the square root of (width squared plus height squared), divided by the diagonal in inches. A 27 inch 4K monitor has 3,840 by 2,160 pixels, so its diagonal is the square root of (3,840 squared plus 2,160 squared), which is 4,406 pixels. Divide 4,406 by 27 and you get 163 ppi.

Two related numbers come out of the same measurement. Dot pitch is the distance between the centers of two neighboring pixels, and it is 25.4 divided by PPI, so that monitor has a dot pitch of 0.156 mm. Total pixels is width times height, or 8.29 million here, which is the figure shoppers compare when they say 4K. The inch itself is defined as exactly 25.4 millimeters by international agreement, and NIST publishes the unit definitions that the conversion rests on.

PPI is not DPI. Dots per inch belongs to printing, where a printer lays down ink dots, and a 300 dpi print is a different measurement from a 300 ppi screen. The two get mixed up because both describe how finely an image is sampled, but a screen pixel is a fixed square of light and a printer dot is a spot of ink that can overlap its neighbors.

Seven screens and their real densities

The table runs the same formula on screens people own. Diagonal pixels are rounded to the nearest whole pixel and PPI to one decimal place.

The spread is wide. A 24 inch 1080p monitor sits at 91.8 ppi, and a 27 inch 4K panel at the same desk sits at 163.2 ppi, which is 78 percent more pixels per inch from the same chair. A 6.1 inch phone reaches 461 ppi, five times the desktop monitor and more than twice the laptop.

None of those numbers says which screen looks better. They say how close the pixel grid is, and the eye cares about something else: how much of your field of view a single pixel covers.

Why a 460 ppi phone does not look harsh

A phone held 12 inches away is a small object in your visual field. Its 2,556 pixels spread across a 5.6 inch width each subtend about 0.62 arcminutes of view, so the grid is finer than the eye can resolve at that distance. The 163 ppi monitor at 24 inches has each pixel subtending 0.88 arcminutes, which is coarser, so the monitor is the one with visible pixels, not the phone.

Convert that to pixels per degree and the comparison gets clear. The phone shows about 97 pixels per degree, the 27 inch 4K monitor about 68, and a 55 inch 4K television at 9 feet about 151. The eye resolves roughly 60 pixels per degree at 20/20 acuity, so all three are past the point where a single pixel can be picked out.

Once a screen passes that threshold, extra pixels stop adding sharpness and start adding something else: room for smaller text, more content on screen, or a wider color gamut. The phone does not look harsh because its pixels are invisible at 12 inches. It looks small, which is a different complaint, and that is why phone interfaces scale text up to two or three times the physical pixel size.

The television number surprises people. At 80 ppi it has the lowest density in the table, yet at couch distance it delivers the highest pixels per degree, because it fills more of your view. Density alone is half the story, and distance is the other half.

The retina threshold and viewing distance

Apple popularized the word retina for displays where individual pixels cannot be distinguished at a normal viewing distance, and the geometry behind it is not Apple specific. Visual acuity of 20/20 means resolving two points about one arcminute apart, which the National Eye Institute describes as the working limit of a healthy eye in its plain language guide to how the eyes work. A pixel smaller than one arcminute of your view is invisible, so the density you need depends entirely on distance.

Set one pixel to one arcminute and solve for density: required PPI = 3,438 divided by viewing distance in inches. At 12 inches that is 287 ppi, at 24 inches 143 ppi, at 30 inches 115 ppi. The table lists the curve.

Turned around, the same rule gives the critical distance: distance in inches = 3,438 / PPI. A 163 ppi monitor stops being retina inside 21 inches, which is why leaning toward a 4K panel at 27 inches brings the pixel grid back. A 461 ppi phone stays retina down to 7.5 inches, closer than anyone holds it.

Apple's own marketing numbers follow the same curve: about 300 ppi at 10 to 12 inches for phones, and 220 ppi at 18 inches for laptops and tablets, which is a little above the 191 ppi the formula asks for. The headroom covers viewers with better than 20/20 vision and the fact that nobody holds a device at a fixed distance.

Scaling changes the PPI your eye receives

Operating systems do not draw at the panel's native density. They draw at a logical resolution and stretch the result, so a 4K panel at 150 percent scaling behaves like a 2,560 by 1,440 screen with larger pixels. Effective PPI is native PPI divided by the scale factor.

That is why a 27 inch 4K monitor at 150 percent behaves like a 108.8 ppi screen for text sizing, even though the panel is 163 ppi. The panel still has the fine grid, so curves, photos and thin lines look smooth, but a 12 point font takes up more physical space. Windows shows the percentage in display settings, and macOS shows the same idea as a "looks like" resolution.

The practical result: a high PPI panel with heavy scaling gives you crisp text at a comfortable size, while a low PPI panel at 100 percent gives you small text with visible stair steps. Two monitors with the same diagonal and the same logical resolution can feel completely different for that reason, and the panel with the higher native density is the one that stays sharp when you zoom in on a photo.

Dot pitch, subpixels and the limits of the number

Dot pitch is PPI expressed in millimeters, and it is the number television reviewers quote. Below 0.2 mm is fine for a desk monitor, 0.25 mm was the standard for years, and 0.3 mm and up is normal on large televisions.

Two panels with the same PPI can still draw text differently, because a pixel is not a single light. An LCD with an RGB stripe has three subpixels side by side in every pixel, so a vertical stem of a letter can land on a subpixel boundary and look sharper than the pixel count suggests. A pentile OLED shares subpixels between neighbors, so its effective resolution for fine colored detail is lower than the spec sheet implies, and small text on a pentile phone can look softer than a cheaper LCD at the same quoted density.

Panel coating, viewing angle, and the way the operating system hints fonts all matter too. PPI sets the ceiling on sharpness. It does not guarantee that a screen reaches the ceiling, and a matte coating on a cheap panel can cost more visible detail than 20 ppi of density gains.

What density to aim for when buying

For a desktop monitor at 24 to 30 inches, 110 ppi is the comfortable floor and 140 to 165 ppi is where text stops showing stair steps. For a laptop at 13 to 16 inches, 200 ppi and up is normal now, and anything under 130 ppi looks dated beside it.

For a television, ignore PPI and work from distance. A 55 inch 4K set at 9 feet gives 151 pixels per degree, well past what the eye can resolve, while a 65 inch 1080p set at 6 feet gives about 43 pixels per degree, where the grid is easy to see on a bright scene. The old advice to sit about 1.5 times the screen height away puts a 4K set right at the edge of visible improvement, and a 1080p set well past it.

For a phone, anything above 300 ppi is beyond the eye at normal holding distance, which is why the phone market stopped advertising the number. For a projector, density is the wrong metric entirely, since the image is spread over a wall and the limiting factor is light output and lens quality.

If you are shopping between two monitors, compare pixels per degree at your actual seating distance rather than PPI. A 32 inch 4K panel at 30 inches and a 27 inch 4K panel at 24 inches both land between 68 and 72 pixels per degree, so they will look about equally sharp even though one is 138 ppi and the other is 163 ppi.

Where PPI tells you nothing

Print is measured in dots per inch, and a 300 dpi print is judged by ink, paper and viewing distance, not by screen density. E-ink readers run at 300 ppi and look nothing like an LCD at the same density, because their pixels reflect light instead of emitting it, and their refresh is measured in hundreds of milliseconds.

The number is also blind to size. A 32 inch 4K monitor and a 15 inch 4K laptop share a pixel count and differ by a factor of two in PPI, so a review that quotes resolution alone has told you half of the story. Put the resolution and the diagonal into the calculator above and the rest follows, including the distance at which the pixels stop being visible.

One last caution: manufacturers sometimes quote "effective" or "simulated" resolution for projectors and TVs that accept a 4K signal but display fewer physical pixels. The panel's native resolution is the only number that belongs in this formula. If the spec sheet says "4K supported" rather than "3,840 x 2,160 native", the density you compute will be wrong.