Question 1

How is a screen's diagonal size measured?

Accepted Answer

Screen size is the diagonal length of the visible display area (corner to corner), measured in inches for the U.S. market and centimeters for the rest of the world. The measurement standard is VESA FPDM 2.0 (Flat Panel Display Measurement Standard, Video Electronics Standards Association) §304.1: diagonal of the active pixel area only, excluding bezels. A 55″ television is 55 inches (139.7 cm) corner to corner of illuminated pixels, not the full outer chassis. The Federal Trade Commission enforcement action against Vizio Inc. (FTC File No. 132-3208, 2017 consent order) required consumer electronics manufacturers to disclose 'measured diagonally' language, which is why every retail listing today reads 'Class 55 (54.6″ measured diagonally)' or similar.

Question 2

How do I compute width and height from diagonal size and aspect ratio?

Accepted Answer

For a rectangular display with diagonal D and aspect ratio W:H, width = D × W / √(W² + H²) and height = D × H / √(W² + H²). Derivation: the Pythagorean theorem (Euclid Book I Proposition 47, c. 300 BCE) gives D² = w² + h²; substituting w = kW and h = kH yields k = D / √(W² + H²). Example: a 65″ TV at 16:9 (the DVB-T/ATSC HDTV standard per ITU-R BT.709-6, 2015 revision) has width = 65 × 16 / √337 ≈ 56.65″ and height = 65 × 9 / √337 ≈ 31.87″. A 27″ monitor at 16:9 has width ≈ 23.53″ and height ≈ 13.24″. A 27″ ultrawide at 21:9 (technically 2560×1080 = 64:27) has width ≈ 24.90″ and height ≈ 10.46″.

Question 3

What is pixels per inch (PPI) and how do I calculate it?

Accepted Answer

Pixels per inch (PPI) — also called pixel density — is the number of pixels per linear inch of display: PPI = √(pixel_width² + pixel_height²) / diagonal_inches. Example: an iPhone 15 Pro at 6.1″ diagonal and 2556×1179 native resolution has PPI = √(2556² + 1179²) / 6.1 = 2814.9 / 6.1 ≈ 461 PPI (Apple's published spec: 460 PPI 'Super Retina XDR'). A 27″ 1440p (2560×1440) monitor has PPI ≈ 108.79. A 27″ 4K UHD (3840×2160) monitor has PPI ≈ 163.18. Apple's 'Retina' branding refers to a PPI × viewing-distance threshold roughly matching 20/20 human visual acuity per Snellen 1862 and Yellott 1982; Steve Jobs introduced the term at WWDC 6 June 2010 for the iPhone 4 (326 PPI at ~10-12″ viewing distance).

Question 4

What viewing distance is recommended for my TV or monitor size?

Accepted Answer

SMPTE Recommended Practice EG-18-1994 (Society of Motion Picture and Television Engineers) recommends a 30° horizontal viewing angle for cinematic immersion (viewing distance ≈ 1.6 × screen width) and a 20° viewing angle for typical home television (viewing distance ≈ 2.5 × screen width). For a 65″ 16:9 TV (56.65″ wide) that yields cinematic distance ≈ 91″ (7.6 ft) and typical distance ≈ 142″ (11.8 ft). THX Certified Cinema (THX Ltd., Lucasfilm 1983) recommends a 36° viewing angle (distance ≈ 1.36 × screen width). For desktop monitors, ergonomic guidelines from the ANSI/HFES 100-2007 standard place the display 20-40 inches from the eyes with the top of the screen at or slightly below eye level.

Question 5

What are the common aspect ratios and where are they used?

Accepted Answer

16:9 (1.78:1) is the ITU-R BT.709 HDTV standard adopted worldwide in 2000 and remains the dominant TV, monitor, and web-video aspect. 16:10 (1.60:1) was the productivity-monitor standard until the industry shift to 16:9 around 2008-2010 and is still used in some Dell/Apple business laptops. 21:9 (2.33:1, actually 64:27 = 2.37:1) is the CinemaScope-adjacent ultrawide monitor format popularized by LG and Samsung after 2013. 32:9 (3.55:1) is Samsung's 'super-ultrawide' since 2017 (2560×1080 or 5120×1440). 4:3 (1.33:1) was the original NTSC/PAL SDTV format (per FCC OET Bulletin 69, 1953-2009 U.S. broadcast standard). 3:2 (1.50:1) is the classic 35 mm still-photography frame (Barnack Leica I 1925) and today's Microsoft Surface laptops. 17:9 (1.90:1) is the DCI 4K native cinema projection format (Digital Cinema Initiatives Specification v1.4, 2018).

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