How do you calculate pixels per inch?

First calculate the diagonal pixel count with the Pythagorean theorem: `sqrt(width^2 + height^2)`. Then divide that diagonal pixel value by the screen diagonal in inches. For a `2560 × 1440` display at `27` inches, the diagonal pixel count is about `2932`, and `2932 ÷ 27 ≈ 108.6 PPI`.

Is this the same as DPI?

For screens, PPI (pixels per inch) and DPI (dots per inch) are often used interchangeably in casual conversation. Strictly speaking, PPI describes digital displays and DPI describes printer dots, but the core idea—density per inch—is similar.

Can I work in centimeters instead of inches?

Yes. Enter the diagonal in inches (you can convert from centimeters by dividing by 2.54), then use the pixels per centimeter output for metric workflows. The width and height in inches can also be multiplied by 2.54 to get centimeters.

Why does my operating system report a different PPI?

Some operating systems infer PPI from EDID data or assume a default value for scaling purposes. If the OS is using an incorrect diagonal size or a scaled resolution, its reported PPI may differ from the true physical PPI calculated from native specs.

Does changing OS scaling or browser zoom affect PPI?

No. PPI is a physical characteristic of the screen. Scaling and zoom only change how many logical pixels your software uses per physical pixel; they do not change how densely pixels are packed on the panel.

How do I know if a screen counts as hiDPI or "retina"?

There is no universal cutoff, but many laptop and phone screens marketed as hiDPI fall in the 200–400+ PPI range. Use the PPI from this calculator to compare options directly rather than relying solely on branding terms.

Can I use this for print design?

You can use the PPI and physical size estimates to compare on‑screen previews to print sizes, but remember that printers often work at much higher DPI (for example, 300–600+). This tool is optimized for displays rather than print devices.

tech calculator

PPI Calculator and Pixel Density Calculator

Find screen PPI, pixel density, and physical display size from resolution and diagonal inches.

Results

Pixels per inch (PPI): 108.79
Pixels per cm: 42.83
Screen width (in): 23.53
Screen height (in): 13.24

Overview

Two screens can share the same resolution but feel completely different to use. A 27-inch 1440p monitor and a 13-inch 1440p laptop technically have the same pixel grid, yet one looks crisp and the other looks huge and chunky. The difference is pixel density: how many pixels are packed into each inch of the display.

That is why people search for a `ppi calculator`, `pixel density calculator`, or even `monitor dpi` and `display dpi`. This route turns your resolution and diagonal screen size into PPI (pixels per inch), pixels per centimeter, and estimated physical width and height so you can compare monitors, laptops, tablets, and phones with real numbers instead of marketing labels.

How to use this calculator

Find the native resolution of your display (for example, 1920×1080, 2560×1440, 3840×2160) and enter the width and height in pixels.
Look up or measure the diagonal size of the screen in inches and enter it into the diagonal size field. Use the viewable area diagonal if it differs from the overall device size.
Click or tab out of the fields to let the calculator compute the diagonal pixel count, PPI, pixels per centimeter, and the physical width and height of the screen.
Compare the PPI value across different displays to see which one will render text and UI elements more sharply. Higher PPI means finer detail, all else equal.
Use the width and height in inches or centimeters to relate digital layouts to physical sizes when testing responsive breakpoints, mockups, or UI components.

Inputs explained

Resolution width (px): The horizontal pixel count of the display’s native resolution, such as 1920, 2560, or 3840. Using native resolution ensures that PPI reflects the actual hardware rather than a scaled mode.
Resolution height (px): The vertical pixel count of the display’s native resolution, such as 1080, 1440, or 2160. Together with the width, this defines the aspect ratio and total pixels on the screen.
Diagonal size (in): The diagonal measurement of the viewable screen area in inches. This is typically what manufacturers advertise (e.g., 24", 27", 32" monitors; 13.3" or 15.6" laptops).

Outputs explained

Pixels per inch (PPI): The number of pixels packed into each inch of the display diagonal. This is the main density metric for comparing how sharp screens of different sizes and resolutions are likely to look.
Pixels per cm: The same density value converted to centimeters instead of inches. This is useful when you work in metric measurements or need to relate display density to physical mockups and print-oriented specs.
Screen width (in): The estimated physical width of the active display area, derived from the horizontal pixel count and calculated PPI. This helps you translate digital layouts into real-world size.
Screen height (in): The estimated physical height of the active display area. Together with the width output, it helps you understand how large UI elements, images, or kiosk components will appear on the actual screen.

How it works

Every rectangular display can be described by its horizontal pixel count, vertical pixel count, and diagonal size in inches. From those three values, you can derive the physical pixel density and the approximate physical dimensions of the active area.

First, the calculator computes the diagonal pixel count using the Pythagorean theorem: diagonalPixels = √(widthPixels² + heightPixels²). This treats the pixel grid as the two legs of a right triangle and the diagonal pixel count as the hypotenuse.

Next, it divides the diagonal pixel count by the diagonal size in inches to get pixels per inch (PPI). This gives you a single measure of how many pixels fit along one inch of the diagonal—higher PPI means smaller, sharper pixels.

With PPI known, the calculator can estimate the physical width and height of the display by dividing the horizontal and vertical pixel counts by PPI. For example, widthInches = widthPixels ÷ PPI and heightInches = heightPixels ÷ PPI.

Pixels per centimeter (px/cm) are derived from PPI using the standard conversion of 1 inch = 2.54 centimeters. Multiplying PPI by 1 ÷ 2.54 gives a density value on a metric scale that is useful for print‑oriented or international workflows.

The math assumes the published diagonal size refers to the viewable portion of the panel, not including bezels. That is how most manufacturers specify monitor and laptop screen sizes, so the derived dimensions usually match reality closely.

Formula

DiagonalPixels = √(ResolutionWidth² + ResolutionHeight²)
PixelsPerInch (PPI) = DiagonalPixels ÷ DiagonalInches
PixelsPerCentimeter = PPI ÷ 2.54
ScreenWidthInches = ResolutionWidth ÷ PPI
ScreenHeightInches = ResolutionHeight ÷ PPI

When to use it

A developer comparing 24‑inch and 27‑inch monitors at the same resolution to see which will make code and UI elements look sharper versus larger and easier to read.
A product designer checking whether a specific PPI qualifies as hiDPI/"retina" for design guidelines and deciding when to export 1x, 2x, or 3x assets.
A UX team mapping breakpoints to physical sizes so that a “mobile” layout matches phones and small tablets accurately during in‑person usability testing.
A photographer or video editor evaluating whether a laptop screen has enough pixel density to judge fine detail without external monitors.

Tips & cautions

Always use the display’s native resolution for PPI calculations. If you enter a scaled resolution from your operating system, you’ll get the effective density of that mode rather than the true physical density.
PPI does not account for viewing distance. A phone at 12 inches and a TV across the room can deliver similar perceived sharpness at different PPIs because you sit farther away from the TV.
Larger PPI values generally mean sharper text and icons but also smaller UI elements at equal scaling. You may need to adjust OS scaling or zoom settings to keep interfaces legible on very high‑density screens.
For print and branding work, compare screen PPI with printer DPI and target print sizes so that on‑screen previews more closely match physical output.
The calculator assumes a perfectly rectangular display with the stated diagonal. Curved monitors and unusual shapes are approximated as flat rectangles, which is usually adequate for density comparisons.
It does not consider operating system scaling factors, browser zoom levels, or application‑specific zoom; it reports physical pixel density only.
Panel quality factors such as contrast, color gamut, uniformity, response time, and HDR support are outside the scope of this tool. Two displays with identical PPI can still differ significantly in perceived quality.
Very small published diagonals that include rounded corners or camera cutouts may produce slight differences between the calculated width/height and the exact usable area.

Worked examples

27‑inch 2560×1440 (QHD) monitor

Resolution = 2560×1440; diagonal size = 27 inches.
DiagonalPixels ≈ √(2560² + 1440²) ≈ 2,932 pixels.
PPI ≈ 2,932 ÷ 27 ≈ 108.6 pixels per inch.
ScreenWidth ≈ 2560 ÷ 108.6 ≈ 23.6 inches; ScreenHeight ≈ 1440 ÷ 108.6 ≈ 13.3 inches.
You can compare this PPI to other monitors to see whether text will look finer or coarser.

13‑inch 4K (3840×2160) laptop

Resolution = 3840×2160; diagonal size = 13 inches.
DiagonalPixels ≈ √(3840² + 2160²) ≈ 4,414 pixels.
PPI ≈ 4,414 ÷ 13 ≈ 339 PPI, which is firmly in hiDPI/"retina" territory.
At this density, most operating systems apply scaling (for example, 200%) so text stays readable.

Comparing a 24‑inch 1080p monitor to a 27‑inch 1080p monitor

Both displays share a 1920×1080 resolution but have different diagonals.
For 24 inches, PPI ≈ √(1920² + 1080²) ÷ 24 ≈ 92 PPI.
For 27 inches, PPI ≈ √(1920² + 1080²) ÷ 27 ≈ 82 PPI.
The larger 27‑inch screen will make everything appear physically bigger but slightly less sharp at the same viewing distance.

Deep dive

This route works as both a `ppi calculator` and a pixel density calculator. Enter screen resolution and diagonal size to see pixels per inch, pixels per centimeter, and approximate physical display dimensions so you can compare sharpness with hard data instead of vague marketing labels.

It is particularly useful for designers and developers who care about hiDPI support, vector rendering, and how interfaces scale across devices. By understanding PPI, you can choose appropriate asset scales, tune CSS breakpoints, and pick screens that balance clarity with comfortable text size for long coding or reading sessions.

Because the tool exposes both PPI and physical width/height, it also helps teams planning usability tests or kiosk interfaces that must hit certain physical dimensions on specific devices.

The page also answers related search intent such as `pixels per inch calculator`, `how to calculate pixels per inch`, and `monitor dpi` by showing the actual formula behind the result instead of treating display density like a black box.

Methodology & assumptions

The calculator reads a display’s horizontal resolution, vertical resolution, and diagonal size in inches.
It computes the diagonal pixel count using the Pythagorean theorem: `sqrt(width^2 + height^2)`.
Pixels per inch are calculated as `Diagonal pixels ÷ Diagonal inches`.
Pixels per centimeter are calculated as `PPI ÷ 2.54`, using the standard inch-to-centimeter conversion.
Estimated physical display width and height are calculated as `Resolution width ÷ PPI` and `Resolution height ÷ PPI`.
The route assumes the manufacturer’s published diagonal refers to the active display area and that the screen behaves like a flat rectangle.
Copy on the page is kept aligned with `pixelDensityCalculator` so the examples, formula, and FAQs describe the live computation accurately.

Sources

Android Developers — Support different pixel densitiesUsed for official display-density terminology and the distinction between physical pixel density and density-independent UI concepts.
MDN Web Docs — Window: devicePixelRatio propertyUsed for source-backed framing that physical pixels and software scaling are different concepts.
NIST Guide to the SI — Appendix B: Conversion FactorsUsed for the inch-to-centimeter conversion applied when deriving pixels per centimeter.

FAQs

How do you calculate pixels per inch?: First calculate the diagonal pixel count with the Pythagorean theorem: `sqrt(width^2 + height^2)`. Then divide that diagonal pixel value by the screen diagonal in inches. For a `2560 × 1440` display at `27` inches, the diagonal pixel count is about `2932`, and `2932 ÷ 27 ≈ 108.6 PPI`.
Is this the same as DPI?: For screens, PPI (pixels per inch) and DPI (dots per inch) are often used interchangeably in casual conversation. Strictly speaking, PPI describes digital displays and DPI describes printer dots, but the core idea—density per inch—is similar.
Can I work in centimeters instead of inches?: Yes. Enter the diagonal in inches (you can convert from centimeters by dividing by 2.54), then use the pixels per centimeter output for metric workflows. The width and height in inches can also be multiplied by 2.54 to get centimeters.
Why does my operating system report a different PPI?: Some operating systems infer PPI from EDID data or assume a default value for scaling purposes. If the OS is using an incorrect diagonal size or a scaled resolution, its reported PPI may differ from the true physical PPI calculated from native specs.
Does changing OS scaling or browser zoom affect PPI?: No. PPI is a physical characteristic of the screen. Scaling and zoom only change how many logical pixels your software uses per physical pixel; they do not change how densely pixels are packed on the panel.
How do I know if a screen counts as hiDPI or "retina"?: There is no universal cutoff, but many laptop and phone screens marketed as hiDPI fall in the 200–400+ PPI range. Use the PPI from this calculator to compare options directly rather than relying solely on branding terms.
Can I use this for print design?: You can use the PPI and physical size estimates to compare on‑screen previews to print sizes, but remember that printers often work at much higher DPI (for example, 300–600+). This tool is optimized for displays rather than print devices.

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This pixel density calculator estimates screen PPI and physical dimensions based on user‑supplied resolution and diagonal size. It does not measure your actual device or account for manufacturer quirks, panel defects, or operating system scaling. Use these values as a planning and comparison aid, and always verify critical specifications with the device manufacturer or official documentation.