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03 // Bidirectional STEM Calculators // EVERYDAYPPI = √(W_px² + H_px²) / D_in

Display Pixel Density (PPI) & Screen Diagonal Calculator

Display Pixel Density (PPI) divides the Pythagorean diagonal pixel count √(W_px² + H_px²) by the physical diagonal screen measurement D_in in inches.

PPI = √(W_px² + H_px²) / D_in
Pick which value you want to calculate (or type into any field):Solving for: PPI — Pixel Density (Pixels Per Inch)
Calculated

Linear pixels per inch (Retina desktop ≈ 218 PPI)

201,500.00
unit

Horizontal pixel columns

10016,384.00
unit

Vertical pixel rows

10016,384.00
unit

Corner-to-corner physical panel size in inches

1200
unit
Calculated Result · Pixel Density (Pixels Per Inch) (PPI)
163.1783

Step-by-Step Calculation

01Canonical Law: PPI = √(W_px² + H_px²) / D_in
02Given Inputs (Base Units): W_px = 3,840, H_px = 2,160, D (in) = 27
03Solve for PPI (Pixel Density (Pixels Per Inch)): PPI = 163.18

Display Pixel Density (PPI) divides the Pythagorean diagonal pixel count √(W_px² + H_px²) by the physical diagonal screen measurement D_in in inches.

Real-World Reference Values

macOS Non-Retina / 2× HiDPI Sweet Spot109 PPI (1×) / 218 PPI (2×)

27-inch 5K (5120×2880) hits 217.6 PPI

27-inch 4K UHD Monitor163.2 PPI (4,405.8 diag px)

8.29 Megapixels total (3840 × 2160)

Flagship OLED Smartphone450 – 510 PPI

Viewed at 25–30 cm reading distance

20-Row Comparison Table

Pixel Density (Pixels Per Inch) (PPI) · Horizontal Resolution (px) (W_px)

Display Pixel Density (PPI) & Screen Diagonal Calculator — Horizontal Resolution (px) → Pixel Density (Pixels Per Inch)
#Horizontal Resolution (px) (W_px)Pixel Density (Pixels Per Inch) (PPI)Δ %
011,420.80 95.7554 -41.32%
021,703.75 101.8913 -37.56%
031,986.69 108.6932 -33.39%
042,269.64 116.044 -28.89%
052,552.59 123.8462 -24.10%
062,835.54 132.0196 -19.09%
073,118.48 140.4995 -13.90%
083,401.43 149.2337 -8.55%
093,684.38 158.18 -3.06%
103,840.00 Current163.1783 0.00%
114,250.27 176.5794 +8.21%
124,533.22 185.9823 +13.97%
134,816.17 195.4948 +19.80%
145,099.12 205.1015 +25.69%
155,382.06 214.7899 +31.63%
165,665.01 224.5494 +37.61%
175,947.96 234.371 +43.63%
186,230.91 244.2473 +49.68%
196,513.85 254.172 +55.76%
206,796.80 264.1395 +61.87%
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Frequently Asked Questions

What is Dot Pitch in millimeters from PPI?+

Pixel dot pitch (center-to-center distance between adjacent pixels) equals 25.4 / PPI millimeters (at 163.2 PPI, dot pitch is 0.1556 mm).

Why do macOS designers target 110 PPI or 220 PPI monitors?+

macOS window server renders UI elements assuming ~109 PPI (1×) or ~218 PPI (2× Retina), avoiding fractional GPU downsampling.

How is angular visual acuity related to PPI and viewing distance?+

A 20/20 human eye resolves 1 arcminute (1/60°), so the Retina threshold PPI at viewing distance d (inches) is PPI ≥ 3438 / d.