Answer first
What this calculator tells you
Calculate a screen's pixel density and pixel pitch from its resolution and diagonal size. Compare monitors and phones by sharpness, not by resolution alone. Formula: PPI = √(width² + height²) ÷ diagonal size in inches; pixel pitch (mm) = 25.4 ÷ PPI. At the worked-example inputs, the pixels per inch is 108.8. Holding every other input steady, moving horizontal resolution (pixels) from 2,048 to 3,072 moves the result from 92.7 to 125.7.
Transparent method
The formula
Compare monitors and phones by sharpness, not by resolution alone.
Worked example
Example inputs
How to interpret the result
Sharpness on a screen depends on how many pixels fit into each inch, not on the resolution number alone. A 27-inch monitor with 2560 by 1440 pixels packs about 109 per inch, while the same resolution on a 32-inch panel spreads to about 92. The pixel pitch output gives the same idea as a distance, roughly 0.23 millimeters between pixel centers here.
At the worked-example inputs the pixels per inch is 108.8. It rises with horizontal resolution (pixels) and vertical resolution (pixels) and falls as screen diagonal (inches) increases.
Password crack-time figures assume one specific guessing speed and no other weakness such as reuse, a data breach or a guessable personal pattern; a real attacker's actual speed and method can differ substantially. Subnet, transfer-time and storage figures are exact defined arithmetic, but a device, ISP or operating system may report a size or speed using a different unit convention (decimal or binary) than the one selected here.
Before you rely on it
What to check
Measure the diagonal of the visible screen. Advertised sizes are rounded, and a half-inch difference shifts the density by a few percent.
The common error
Where people go wrong with PPI (pixels per inch) calculator
Comparing resolutions across different screen sizes. A phone with fewer pixels can look far sharper than a larger display with more, because the pixels are packed tighter.
Sensitivity evidence
How horizontal resolution (pixels) changes the pixels per inch
Holding every other input at the worked-example value, moving horizontal resolution (pixels) from 2,048 to 3,072 moves the pixels per inch from 92.7 to 125.7: a spread of 32.9, or 30% of the worked-example result.
| Horizontal resolution (pixels) | Pixels per inch | Pixel pitch (mm) |
|---|---|---|
| 2,048 | 92.7 | 0.274 |
| 2,304 | 100.6 | 0.252 |
| 2,560worked example | 108.8 | 0.233 |
| 2,816 | 117.1 | 0.217 |
| 3,072 | 125.7 | 0.202 |
Every input, tested
Which input moves the pixels per inch most
Of the 3 inputs, screen diagonal (inches) moves the pixels per inch most (24.5 across the range tested) and vertical resolution (pixels) moves it least (5.2).
| Input | Tested from | To | Pixels per inch at each end | Swing |
|---|---|---|---|---|
| Screen diagonal (inches) | 24 | 30 | 122.4 to 97.9 | 24.5 (23%) |
| Horizontal resolution (pixels) | 2,304 | 2,816 | 100.6 to 117.1 | 16.5 (15%) |
| Vertical resolution (pixels) | 1,296 | 1,584 | 106.3 to 111.5 | 5.2 (4.8%) |
Two variables at once
Pixels per inch by horizontal resolution (pixels) and vertical resolution (pixels)
Across the grid the pixels per inch runs from 87 to 130.5. Moving horizontal resolution (pixels) from 2,048 to 3,072 shifts it by 32.9 at the middle column, and moving vertical resolution (pixels) from 1,152 to 1,728 shifts it by 10.4 at the middle row, so horizontal resolution (pixels) is the bigger lever here.
| Horizontal resolution (pixels) \ Vertical resolution (pixels) | 1,152 | 1,440 | 1,728 |
|---|---|---|---|
| 2,048 | 87 | 92.7 | 99.2 |
| 2,304 | 95.4 | 100.6 | 106.7 |
| 2,560 | 104 | 108.8 | 114.4 |
| 2,816 | 112.7 | 117.1 | 122.4 |
| 3,072 | 121.5 | 125.7 | 130.5 |
The highlighted cell is the worked example: 108.8.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Horizontal resolution (pixels) | 2,560 | Enter the horizontal resolution (pixels) used in this calculation. |
| Vertical resolution (pixels) | 1,440 | Enter the vertical resolution (pixels) used in this calculation. |
| Screen diagonal (inches) | 27 | Enter the screen diagonal (inches) used in this calculation. |
| Pixels per inch | 108.8 | |
| Pixel pitch (mm) | 0.233 | |
Inputs, definitions and assumptions
Horizontal resolution (pixels)
Enter the horizontal resolution (pixels) used in this calculation. The prefilled worked-example value is 2,560.
Vertical resolution (pixels)
Enter the vertical resolution (pixels) used in this calculation. The prefilled worked-example value is 1,440.
Screen diagonal (inches)
Enter the screen diagonal (inches) used in this calculation. The prefilled worked-example value is 27.
How to use this calculator
- 1Verify the inputs. Gather horizontal resolution (pixels), vertical resolution (pixels) and screen diagonal (inches) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the pixels per inch at 108.8. Store your own version of it as Scenario A.
- 3Test one change. Start with screen diagonal (inches), the input with the biggest effect here: moving screen diagonal (inches) from 24 to 30 takes the pixels per inch from 122.4 to 97.9, a swing of 23% of the worked-example figure.
- 4Check the extremes. At half the example screen diagonal (inches) (13.5) the pixels per inch is 217.6; at double (54) it is 54.4.
People also ask
Frequently asked questions
How do you calculate PPI (pixels per inch)?
PPI = √(width² + height²) ÷ diagonal size in inches; pixel pitch (mm) = 25.4 ÷ PPI. At the worked-example inputs the pixels per inch is 108.8.
What does the PPI (pixels per inch) result mean?
Compare monitors and phones by sharpness, not by resolution alone. At the worked-example inputs the pixels per inch is 108.8. It rises with horizontal resolution (pixels) and vertical resolution (pixels) and falls as screen diagonal (inches) increases.
How much does horizontal resolution (pixels) change the pixels per inch?
Holding every other input at the worked-example value, moving horizontal resolution (pixels) from 2,048 to 3,072 moves the pixels per inch from 92.7 to 125.7, a spread of 32.9.
What are the limits of this PPI (pixels per inch) calculator?
Password crack-time figures assume one specific guessing speed and no other weakness such as reuse, a data breach or a guessable personal pattern; a real attacker's actual speed and method can differ substantially. Subnet, transfer-time and storage figures are exact defined arithmetic, but a device, ISP or operating system may report a size or speed using a different unit convention (decimal or binary) than the one selected here. The tables on this page test horizontal resolution (pixels) only from 2,048 to 3,072; a value outside that range is not tabulated here.
Which input moves the pixels per inch most in the PPI (pixels per inch) calculator?
Ranked by how far each moves the pixels per inch across the range tested: screen diagonal (inches) (24.5, 23%), horizontal resolution (pixels) (16.5, 15%) and vertical resolution (pixels) (5.2, 4.8%).
If I double screen diagonal (inches) in the PPI (pixels per inch) calculator, does the pixels per inch double?
Doubling it from 27 to 54 takes the pixels per inch from 108.8 to 54.4, which is 0.50 times the worked-example figure. So it falls instead of rising. Halving it to 13.5 gives 217.6.
How much does vertical resolution (pixels) matter in the PPI (pixels per inch) calculator?
The worked example uses 1,440. With the other inputs left at the worked example, moving vertical resolution (pixels) from 1,296 to 1,584 takes the pixels per inch from 106.3 to 111.5, a swing of 4.8% of the worked-example figure.
How much does screen diagonal (inches) matter in the PPI (pixels per inch) calculator?
The worked example uses 27. With the other inputs left at the worked example, moving screen diagonal (inches) from 24 to 30 takes the pixels per inch from 122.4 to 97.9, a swing of 23% of the worked-example figure.
Which inputs change the pixel pitch (mm) in the PPI (pixels per inch) calculator?
At the worked-example inputs it is 0.233. Horizontal resolution (pixels) takes it from 0.252 to 0.217, vertical resolution (pixels) takes it from 0.239 to 0.228 and screen diagonal (inches) takes it from 0.208 to 0.259.
Why does a /24 subnet only give 254 usable addresses instead of 256?
The first address in the range is reserved as the network address and the last as the broadcast address, neither of which can be assigned to a device. A /24 has 256 total addresses, so subtracting those two reserved ones leaves 254 usable hosts.
Is a longer password always better than a more complex one?
Length increases entropy faster than adding character types does, because entropy grows with the length exponent, not the pool size. A 16-character password using only lowercase letters can have more entropy than an 8-character password mixing every character type, while also being easier to remember.
Why do IPv4 addresses top out at 255 per octet?
Each octet is 8 bits, and 8 bits can represent 256 distinct values, 0 through 255. That ceiling is fixed by the IPv4 standard's 32-bit address size, split into four 8-bit octets, not an arbitrary limit.
Sources and evidence
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