PPI calculator: pixel density from resolution and diagonal, plus screen width and height, aspect ratio, dot pitch and the distance where pixels blend.
업데이트 검증한 예제: 5
A 27-inch 2,560 × 1,440 screen (16:9) packs 108.8 pixels per inch into a 23.5 × 13.2 in panel; beyond about 32 in (80 cm) a person with 20/20 vision can't pick out single pixels.
At this distance one pixel spans 1 arcminute, the detail 20/20 vision resolves; this is the idea behind “retina” displays.
Pixel density is the diagonal resolution in pixels divided by the diagonal size in inches: PPI = √(w² + h²) ÷ diagonal. The same ratio splits the diagonal into the physical width and height, dot pitch is 25.4 mm ÷ PPI, and the blend distance is where one pixel spans 1 arcminute, the detail that 20/20 vision resolves.
The default 27-inch 2560 × 1440 monitor has 108.79 PPI, a 16:9 panel of 23.53 × 13.24 inches, and pixels that blend beyond about 31.6 inches (80 cm). The same size at 4K, 3840 × 2160, reaches 163.18 PPI and blends beyond 21 inches.
Advertised diagonals are rounded, so results can differ slightly from a spec sheet. The blend distance assumes 20/20 vision; people with sharper eyesight can pick out pixels from further away.
검증 출처: Python decimal: √(2560² + 1440²)/27; retina distance 1/(PPI·tan(π/10800))
검증 출처: Apple MacBook Air (M1, 2020) tech specs list 227 ppi; Python decimal gives 226.983
검증 출처: Python decimal: 1000√2/10
검증 출처: Python decimal and math.gcd: gcd(1366, 768) = 2
Find the diagonal in pixels with Pythagoras and divide it by the diagonal in inches. A 27-inch 2560 × 1440 monitor has √(2560² + 1440²) = 2,937.2 pixels along the diagonal, so 2,937.2 ÷ 27 = 108.79 PPI. Use the visible screen diagonal, not the outside of the case.
Apple introduced the name with the iPhone 4 in 2010: a 960 × 640 screen at 326 pixels per inch, where Apple said the eye cannot make out individual pixels at a normal viewing distance. At 326 PPI one pixel spans 1 arcminute from 10.5 inches, so the threshold depends on distance: a 27-inch 4K monitor at 163 PPI passes the same test from 21 inches.
To stop seeing single pixels with 20/20 vision, sit at least about 43 inches (1.1 m) from a 55-inch 4K TV, which has 80.1 PPI, or 51 inches (1.3 m) from a 65-inch one. Beyond about 86 inches (2.2 m), a 55-inch 1080p screen blends its pixels too, so 4K adds little visible detail from that far away.
16:9: divide both numbers by their greatest common divisor, 160. TVs and most monitors are 16:9, while some laptops use 16:10, such as the 13.3-inch 2560 × 1600 MacBook Air (8:5 when reduced). A resolution such as 1366 × 768 reduces only to 683:384, which is within 0.05% of 16:9.
Advertised diagonals are rounded. The iPhone 4's 960 × 640 screen is sold as 3.5 inches, which gives 329.7 PPI, while Apple quotes 326 PPI, matching a diagonal of about 3.54 inches. Enter the diagonal to two decimal places when you know it, and check that the resolution is the panel's native one.
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Pixel density — PPI from resolution and diagonal; Visual acuity — 20/20 vision resolves detail of 1 arcminute.
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