PPI calculator: pixel density from resolution and diagonal, plus screen width and height, aspect ratio, dot pitch and the distance where pixels blend.
Aktualisiert Geprüfte Beispiele: 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.
Prüfquelle: Python decimal: √(2560² + 1440²)/27; retina distance 1/(PPI·tan(π/10800))
Prüfquelle: Apple MacBook Air (M1, 2020) tech specs list 227 ppi; Python decimal gives 226.983
Prüfquelle: Python decimal: 1000√2/10
Prüfquelle: 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.
Die Genauigkeit hängt von Ihren Eingaben und den Annahmen der Methode ab. Die Dezimalrechnung nutzt 50 signifikante Stellen, doch Schätzungen, numerische Verfahren und Quelldaten können ungenauer sein. Die angezeigte Rundung beseitigt diese Grenzen nicht. Anhand unabhängiger Quellen geprüfte Rechenbeispiele: 5. Beispielsweise wird „27-inch 2560 × 1440 monitor“ anhand von Python decimal: √(2560² + 1440²)/27; retina distance 1/(PPI·tan(π/10800)) geprüft.
Pixel density — PPI from resolution and diagonal; Visual acuity — 20/20 vision resolves detail of 1 arcminute.
Dieser Rechner enthält 5 Rechenbeispiele mit Ergebnissen aus unabhängigen Quellen. Sie laufen in der Testsuite und können auch hier ausgeführt werden.