PPI Calculator: Screen Size, TV Viewing Distance and FOV

Find optimal 4K/OLED TV screen sizes and seating distances according to THX/SMPTE guidelines and calculate monitor pixel density (PPI).

Screen dimensions, PPI and viewing distance: the formulas

Pixel density is PPI = √(width² + height² in pixels) ÷ diagonal in inches: a 65-inch 4K TV shows 68 PPI, a 27-inch 4K monitor 163 PPI. Viewing distance comes from the viewing angle: width × 1.37 for a 40° field (THX guideline), width × 1.87 for 30° (SMPTE guideline), i.e. 1.98 m and 2.69 m for a 65-inch 16:9 screen.

Formulas

  • Width = diagonal × w ÷ √(w² + h²) and height = diagonal × h ÷ √(w² + h²), where w:h is the aspect ratio (16:9, 21:9, 32:9, 16:10 or 4:3).
  • PPI = √(horizontal pixels² + vertical pixels²) ÷ diagonal; dot pitch (mm) = 25.4 ÷ PPI.
  • "Cinema" distance = width ÷ (2 × tan 20°) = width × 1.3737; "standard" distance = width ÷ (2 × tan 15°) = width × 1.866.
  • Displayed acuity limit = height ÷ (1,080 × tan 1 arcminute) ≈ 3.18 × screen height, the distance at which a 1080p pixel covers only one arcminute.

Example: 65-inch 4K TV, 16:9

The screen measures 143.9 × 80.9 cm (1.16 m²). Its 4,406-pixel diagonal divided by 65 gives 68 PPI, with a 0.375 mm dot pitch. 40° distance: 1.98 m; 30° distance: 2.69 m; acuity limit: 2.58 m. The other way round, a sofa at 2.5 m calls for an 82-inch diagonal at 40° and 61 inches at 30°. For comparison, a 27-inch monitor goes from 109 PPI at 1440p to 163 PPI at 4K.

Good to know

The 40° and 30° angles are guidelines from a vendor and an engineering society, not standards for a living room. The 30° figure comes from an SMPTE guide for cinema theatres, withdrawn in 2003; THX's rule (diagonal = distance × 0.835) works out at about 40° in 16:9. The acuity limit does not depend on the resolution you pick: beyond it, a 1 arcminute eye can no longer tell a 4K picture from a 1080p one, whose pixels blend at 3.2 times the screen height; 4K pixels already blend beyond 1.6 times. This tool works as a technical sheet (monitors, ultrawide formats, PPI); to pick a TV size from your sofa distance quickly, the TV size calculator gives a range in inches.

Sources and dates: THX, "What size TV should I buy for my living room?" (distance × 0.835 rule, article dated 28/05/2020); SMPTE EG 18-1994, Design of Effective Cine Theaters (screen filling about 30° of the horizontal field; withdrawn 26/03/2003) (checked 14/10/2026)

Frequently Asked Questions

How many PPI does a 27-inch monitor have?

A 27-inch 16:9 screen shows 82 PPI at 1080p, 109 PPI at 1440p and 163 PPI at 4K. The formula divides the pixel diagonal by the diagonal in inches.

How far should I sit from a 65-inch TV?

With a 16:9 screen 143.9 cm wide, the tool gives 1.98 m for a 40° field (THX guideline) and 2.69 m for 30° (SMPTE guideline). Which one suits you depends on use: films or everyday viewing.

How do I get the real width of a screen from its diagonal?

Multiply the diagonal by w ÷ √(w² + h²) for the aspect ratio. In 16:9 the factor is 0.872: a 55-inch screen is about 121.8 cm wide and 68.5 cm high, without bezels.

At what distance can you no longer tell 4K from 1080p?

With 1 arcminute acuity, 1080p pixels become invisible beyond about 3.2 times the screen height. This is the acuity limit the tool shows: 2.58 m for a 65-inch 16:9 TV.

Is this tool really free?

Yes, all tools on Kristools are 100% free and accessible without registration.

Is my data protected?

Yes. All processing is performed directly and securely inside your browser. No personal data is sent to our servers.