# PPI calculator for screen size and aspect ratio

> PPI calculator: pixel density from resolution and diagonal, plus screen width and height, aspect ratio, dot pitch and the distance where pixels blend.

النسخة التفاعلية: https://www.calcopenly.com/ar/everyday/screen-size-ppi-calculator
الموضوع: حاسبات الحياة اليومية

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.

## المدخلات

- **Diagonal**
- **Horizontal pixels**
- **Vertical pixels**

## النتائج

- Pixel density (PPI) — النتيجة الرئيسية
- نسبة الأبعاد
- العرض (in)
- الارتفاع (in)
- العرض (cm)
- الارتفاع (cm)
- Dot pitch (mm)
- Total pixels (MP)
- Pixels blend beyond (in)
- Pixels blend beyond (cm)

## الصيغة

$$
\begin{gathered}\text{PPI} = \frac{\sqrt{w^2 + h^2}}{\text{diagonal (in)}} \\ d_{\text{blend}} = \frac{1}{\text{PPI}\cdot\tan(1')}\end{gathered}
$$

## أمثلة محلولة

### 27-inch 2560 × 1440 monitor

- Diagonal: 27 in
- Horizontal pixels: 2560
- Vertical pixels: 1440
- **Pixel density: 108.79 PPI**
- **نسبة الأبعاد: 16:9**
- **العرض: 23.53 in**
- **الارتفاع: 13.24 in**
- **Dot pitch: 0.2335 mm**
- **Pixels blend beyond: 31.6 in**
- **Total pixels: 3.69 MP**
- مصدر التحقق: ⁨Python decimal: √(2560² + 1440²)/27; retina distance 1/(PPI·tan(π/10800))⁩

### 13.3-inch 2560 × 1600 laptop

- Diagonal: 13.3 in
- Horizontal pixels: 2560
- Vertical pixels: 1600
- **Pixel density: 227.00 PPI**
- **نسبة الأبعاد: 8:5 (16:10)**
- مصدر التحقق: ⁨Apple MacBook Air (M1, 2020) tech specs list 227 ppi; Python decimal gives 226.983⁩

### Square screen

- Diagonal: 10 in
- Horizontal pixels: 1000
- Vertical pixels: 1000
- **Pixel density: 141.42 PPI**
- **نسبة الأبعاد: 1:1**
- **العرض: 7.07 in**
- مصدر التحقق: ⁨Python decimal: 1000√2/10⁩

### 1366 × 768 is only nearly 16:9

- Diagonal: 15.6 in
- Horizontal pixels: 1366
- Vertical pixels: 768
- **Pixel density: 100.45 PPI**
- **نسبة الأبعاد: 683:384 (≈ 16:9)**
- مصدر التحقق: ⁨Python decimal and math.gcd: gcd(1366, 768) = 2⁩

### Diagonal given in centimetres

- Diagonal: 68.58 cm
- Horizontal pixels: 2560
- Vertical pixels: 1440
- **Pixel density: 108.79 PPI**
- مصدر التحقق: ⁨68.58 cm = 27 in exactly; same as the 27-inch example⁩

## الأسئلة

### How do you calculate PPI?

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.

### What PPI counts as a Retina display?

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.

### How far should I sit from a 4K TV?

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.

### What aspect ratio is 2560 × 1440?

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.

### Why does my result differ from the spec sheet?

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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### ما مصدر هذه الطريقة؟

Pixel density — PPI from resolution and diagonal; Visual acuity — 20/20 vision resolves detail of 1 arcminute.

## المصادر

- [Pixel density — PPI from resolution and diagonal](https://en.wikipedia.org/wiki/Pixel_density)
- [Visual acuity — 20/20 vision resolves detail of 1 arcminute](https://en.wikipedia.org/wiki/Visual_acuity)