How to Calculate PPI from Screen Size and Resolution (with Examples)

The math to compute pixels per inch (PPI) from a screen's diagonal and resolution is one line of high-school geometry. This guide walks the formula through, then runs five worked examples on real devices so the numbers feel concrete. If you'd rather skip the arithmetic, our free PPI calculator takes the inputs and returns the answer in under a second.

The formula

You need two measurements:

• Diagonal of the visible screen area, in inches. Manufacturers always quote this; for an unknown panel a tape measure works.
• Resolution in physical pixels — width × height. For a phone or tablet this is the native panel resolution; for a laptop or monitor it's the resolution at which the screen runs without DPI scaling.

The pixel diagonal is Pythagoras's hypotenuse:

pixel_diagonal = √(width_px² + height_px²)

PPI is that pixel diagonal divided by the inch diagonal:

PPI = pixel_diagonal ÷ diagonal_inches

Combining the two:

PPI = √(width_px² + height_px²) ÷ diagonal_inches

That's the entire calculation. Every "PPI calculator" on the internet implements this formula. Most of the variation comes from how each tool handles input parsing, edge cases, and whether it can also tell you whether the answer counts as Retina at your viewing distance.

Worked example 1 — iPhone 15 Pro

Apple's 2023 flagship lists a 6.1-inch display with a native resolution of 1179 × 2556. Plugging in:

pixel_diagonal = √(1179² + 2556²)
              = √(1,389,841 + 6,533,136)
              = √7,922,977
              ≈ 2814.78
PPI = 2814.78 ÷ 6.1
   ≈ 461 PPI

Apple's spec sheet rounds to 460. The single-pixel discrepancy is from the diagonal being quoted to the nearest tenth of an inch; the real visible diagonal is closer to 6.12 in. At 461 PPI on a phone held 30 cm away, this clears the Retina threshold by more than 50 percent — comfortably pixel-free.

Worked example 2 — MacBook Pro 14"

The 2023 MacBook Pro 14-inch ships a 14.2-inch panel at 3024 × 1964:

pixel_diagonal = √(3024² + 1964²)
              = √(9,144,576 + 3,857,296)
              = √13,001,872
              ≈ 3605.81
PPI = 3605.81 ÷ 14.2
   ≈ 254 PPI

At 60 cm desk distance the Retina threshold is about 145 PPI; this laptop sits well above it. Apple's marketing rounds the panel to 254 PPI, matching exactly. Note that macOS by default runs the panel at half-density "looks-like 1512 × 982" mode for UI scaling — but the underlying pixel count is what determines sharpness.

Worked example 3 — 27-inch 4K monitor

The most common professional monitor configuration in 2026: 27 inches, 3840 × 2160:

pixel_diagonal = √(3840² + 2160²)
              = √(14,745,600 + 4,665,600)
              = √19,411,200
              ≈ 4406
PPI = 4406 ÷ 27
   ≈ 163 PPI

163 PPI is below the 220 PPI Retina baseline but well above the 145 PPI threshold for a 60 cm viewing distance. This is why 27-inch 4K is the sweet spot for a desk monitor: comfortably retina at typical distance, no UI scaling required to keep text legible. The same 4K resolution on a 32-inch monitor drops to 138 PPI — borderline at 60 cm, sharp at 70 cm.

Worked example 4 — iPad Pro 11"

The 11-inch iPad Pro at 2420 × 1668:

pixel_diagonal = √(2420² + 1668²)
              = √(5,856,400 + 2,782,224)
              = √8,638,624
              ≈ 2939
PPI = 2939 ÷ 11.0
   ≈ 267 PPI

Apple lists the iPad as 264 PPI; the small difference comes from the visible 10.86-inch diagonal versus the marketing "11-inch" designation. At a typical tablet viewing distance of 40 cm (between phone and laptop), the Retina threshold is about 218 PPI. The iPad clears it by ~22 percent.

Worked example 5 — Samsung Galaxy S24

The 2024 Galaxy S24 lists 6.2 inches at 1080 × 2340:

pixel_diagonal = √(1080² + 2340²)
              = √(1,166,400 + 5,475,600)
              = √6,642,000
              ≈ 2577.20
PPI = 2577.20 ÷ 6.2
   ≈ 416 PPI

Samsung quotes 416 PPI — exact match. Note this is the FHD+ mode which is the default on the standard S24; the S24 Ultra runs at QHD+ for an even higher density. The standard model still sits above the 30 cm threshold of 291 PPI, so for everyday phone use the resolution difference is invisible to the eye. Samsung's higher-tier phones use QHD+ as a marketing differentiator more than a perceptible upgrade.

Common mistakes

Forgetting to use the physical diagonal, not the bezel-to-bezel measurement. Manufacturers quote the visible area; if you measure your own screen with a tape measure, stay inside the active pixels.

Confusing the panel resolution with the rendered resolution. macOS, Windows, iOS, and Android all scale UI elements relative to the physical panel. The PPI calculation needs the physical resolution (the one the manufacturer lists), not the "looks-like" UI-scaled coordinate the OS reports to applications. On a Retina MacBook the displayed coordinate is half the panel size; on Android with high-DPI scaling it can be a third or less.

Mixing units. Diagonal must be in the same unit as the unit you put under the resolution. Pixels per inch requires inches in the denominator. A diagonal in centimeters needs converting first (divide by 2.54).

Assuming all 4K screens have the same PPI. They don't. Pixel density depends on the diagonal as well as the resolution. A 24-inch 4K is sharper than a 32-inch 4K, which is sharper than a 50-inch 4K. The first is super-retina; the last is below the standard threshold and pixels are visible at typical desk distance.

Using the calculator

Our PPI calculator accepts a diagonal in inches and a resolution string (1920×1080, 3840×2160, or 1179 x 2556 with spaces). The math is identical to the formulas above; the value is in the surrounding context. The calculator additionally returns:

• The sharpness tier (Standard / High / Retina / Super Retina) so you have a one-word answer.
• The Retina threshold at any viewing distance from 20 cm to 3 m, with a slider so you can see how the verdict changes for a phone vs. a TV vs. a projector.
• The physical width and height in inches, derived from the diagonal and resolution aspect ratio — useful if you only know the diagonal and need to compute the actual panel area.
• A one-click handoff to the Screen Ruler tool using the calculated PPI as the calibration value.

For most everyday questions — "how does this monitor's pixel density compare to my phone?" or "is this 4K TV sharp enough at couch distance?" — the calculator returns the answer faster than the manual arithmetic. The formula above is the source of truth; the calculator is the convenience.