Display Mathematics & Formula

PPI Calculator from Inches and Resolution

Pixels Per Inch (PPI) measures the linear pixel density of a digital screen. Learn the exact geometric formula, walk through manual calculations, and compute density for any device.

Calculate Any Screen's PPI

Instant interactive calculation

PPI Calculator

√(W² + H²) ÷ size | PPI ±0.1

Resolution Presets

Device Presets

Resolution width (px)

Resolution height (px)

Screen size

Use the diagonal printed on the box or spec sheet.

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PPI

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Retina estimate

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Dot pitch

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Total pixels

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Megapixels

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Aspect ratio

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Min. distance

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StandardHighUltra HighRetina

See the pixel density

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Higher PPI packs more pixels into the same physical area, producing smaller pixels and finer detail.

Relative Pixel Size:—

Simulated Dot Pitch:—

PPI = √(W² + H²) ÷ diagonal

The PPI Formula Explained

Display screens arrange pixels in a two-dimensional grid. Physical screen size is universally specified by the diagonal measurement in inches. To calculate pixel density along this diagonal, we apply the Pythagorean theorem to the horizontal and vertical pixel counts, then divide by the physical diagonal.

PPI = √(W² + H²) ÷ Diagonal_inches

Mathematical Step-by-Step Breakdown

Step 1: Identify screen dimensions:Find the horizontal resolution (W in pixels), vertical resolution (H in pixels), and physical diagonal (D in inches).
Step 2: Calculate the diagonal resolution in pixels:Square width and height, add them together, and take the square root:
D_pixels = √(W² + H²)
Step 3: Divide diagonal pixels by diagonal inches:Divide the total diagonal pixel count by the screen's physical diagonal:
PPI = D_pixels ÷ D_inches

Step-by-Step Manual Worked Example

Let's calculate the exact pixel density of a 24-inch 1080p desktop monitor (1920 × 1080 resolution, 24.0″ diagonal):

1. Square the pixel dimensions:

19202 = 3,686,400
10802 = 1,166,400

2. Sum the squares:

3,686,400 + 1,166,400 = 4,852,800

3. Take the square root (diagonal in pixels):

√4,852,800 ≈ 2202.907 pixels

4. Divide by diagonal inches:

2202.907 ÷ 24.0 = 91.8 PPI

Common Screen Sizes & Their Calculated PPI

The table below demonstrates how the exact same resolution (like 1080p or 4K) produces completely different pixel densities depending on physical display size:

Device Class / Name	Resolution	Diagonal	Pixel Density	Dot Pitch
6.1″ OLED Smartphone	1170 × 2532	6.1″	457.3 PPI	0.056 mm
15.6″ Full HD Laptop	1920 × 1080	15.6″	141.2 PPI	0.180 mm
24″ 1080p Monitor	1920 × 1080	24″	91.8 PPI	0.277 mm
27″ 1440p Monitor	2560 × 1440	27″	108.8 PPI	0.233 mm
27″ 4K Monitor	3840 × 2160	27″	163.2 PPI	0.156 mm
55″ 4K Television	3840 × 2160	55″	80.1 PPI	0.317 mm

PPI vs. DPI: What Is the Difference?

While people frequently use PPI and DPI interchangeably, they represent two distinct physical media:

PPI (Pixels Per Inch): Measures digital displays. It describes how many glowing RGB sub-pixel clusters exist per linear inch of glass panel.
DPI (Dots Per Inch): Measures physical print technology (inkjet, laser, offset printing). It describes how many microscopic droplets of ink or toner a printer deposits per inch of physical paper.

For a complete deep-dive comparison with visual charts, explore our dedicated PPI vs DPI Difference Guide.

Frequently Asked Questions

How do you calculate PPI from resolution and inches?

To calculate PPI, find the diagonal resolution in pixels using the Pythagorean theorem: D_px = √(Width² + Height²). Then divide the diagonal pixel count by the physical diagonal screen size in inches: PPI = D_px ÷ Diagonal_inches.

What is the difference between screen resolution and PPI?

Resolution is the raw count of pixels across width and height (e.g. 1920×1080 = 2,073,600 total pixels). PPI (Pixels Per Inch) measures pixel density — how tightly those pixels are packed across physical screen space.

Can I calculate PPI if I only have width and height in inches?

Yes. For square-pixel displays (virtually all modern monitors, laptops, and smartphones), horizontal PPI equals Width_pixels ÷ Width_inches, and vertical PPI equals Height_pixels ÷ Height_inches. Both equal the diagonal PPI.

What is a good PPI for monitors, laptops, and phones?

Monitors viewed at arm's length (20–30″) target 100–110 PPI (standard) or 160–220 PPI (Retina/HiDPI). Laptops viewed at 18–24″ typically range between 140 and 260 PPI. Smartphones viewed at 10–12″ require 400+ PPI for indistinguishable pixels.

Why does a 55-inch 4K TV have lower PPI than a 27-inch 4K monitor?

Both displays have identical 3840×2160 pixel grids (8.29 million pixels). Spreading those pixels over 27 inches yields ~163 PPI, while spreading them across 55 inches yields ~80 PPI. However, TVs are viewed from much farther away (6–8 feet), where 80 PPI appears completely sharp.