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TV Viewing Distance Calculator

Converts a TV diagonal into recommended seating distances (THX best-seat 40° and maximum 28° viewing angles, SMPTE 30°, the 1.5–2.5× diagonal rule) and the maximum distance at which 20/20 vision still resolves the full 1080p, 4K or 8K detail; given a seating distance instead, it recommends screen sizes.

When to use

You are choosing a TV size for a room, checking whether a 4K upgrade will be visible from the sofa, or laying out a home cinema.

Do not use when: You need pixel density figures (use screen-ppi) or projector placement (use projector-throw); the results assume a flat 16:9 screen viewed head-on.

Formula

width = diagonal × a / √(a² + 1) with a = aspect ratio; distance(θ) = width / (2 × tan(θ / 2)) for θ = 40°, 28°, 30°; rule = 1.5 × diagonal … 2.5 × diagonal; full_resolution_distance = width / (pixels_wide × tan(1′)); viewing_angle = 2 × atan(width / (2 × distance)); distance mode inverts the same formulas

THX quotes 40° as the best seat and 28° as the farthest recommended seat for home theatre; SMPTE EG-18 recommends at least 30°. The resolution limit uses 1 arcminute per pixel (20/20 acuity): from farther than about 2.2 m a 55-inch 4K set is indistinguishable from 1080p for a viewer with 20/20 vision.

Inputs

Parameter	Type	Unit	Required	Description
`diagonal_inches`	number	in	no	TV diagonal in inches. Give this and/or viewing_distance_m. Range: > 0, ≤ 500
`viewing_distance_m`	number	m	no	Eye-to-screen distance in metres. Given alone, screen sizes are recommended; with the diagonal, the actual viewing angle is reported. Range: > 0, ≤ 50
`resolution`	enum: 1080p \| 4k \| 8k		default 4k	Panel resolution used for the full-detail distance.
`aspect_ratio`	enum: 16:9 \| 21:9 \| 4:3		default 16:9	Width-to-height ratio of the screen or image.

Outputs

Output	Type	Unit	Description
`screen_width_cm`	number	cm	Width of the picture (diagonal mode).
`screen_height_cm`	number	cm	Height of the picture (diagonal mode).
`thx_40deg_m`	number	m	Distance at which the screen spans 40° = width / (2 × tan 20°) ≈ 1.2 × diagonal.
`thx_28deg_m`	number	m	Farthest THX-recommended seat, 28° ≈ 1.75 × diagonal.
`smpte_30deg_m`	number	m	Distance for a 30° field of view ≈ 1.63 × diagonal.
`rule_min_m`	number	m	Near end of the popular 1.5–2.5× diagonal range.
`rule_max_m`	number	m	Far end of the 1.5–2.5× range.
`full_resolution_distance_m`	number	m	Maximum distance at which one pixel of the chosen resolution still subtends 1 arcminute; farther away the extra resolution is invisible to 20/20 vision.
`viewing_angle_deg`	number	°	Horizontal angle the screen subtends at viewing_distance_m (only when both inputs are given).
`recommended_diagonal_thx_in`	number	in	Screen size that spans 40° at viewing_distance_m (distance mode).
`recommended_diagonal_smpte_in`	number	in	Screen size that spans 30° at viewing_distance_m.
`recommended_diagonal_range_in`	string		Range of sizes for which the distance is 1.5–2.5 diagonals.
`min_diagonal_for_resolution_in`	number	in	Diagonal at which the chosen resolution is just fully resolved from viewing_distance_m.

Example

55-inch 4K TV: {"diagonal_inches":55,"resolution":"4k"} → {"screen_width_cm":121.8,"screen_height_cm":68.5,"thx_40deg_m":1.67,"thx_28deg_m":2.44,"smpte_30deg_m":2.27,"rule_min_m":2.1,"rule_max_m":3.49,"full_resolution_distance_m":1.09}

Sofa 3 m from the wall, 4K: {"viewing_distance_m":3,"resolution":"4k"} → {"recommended_diagonal_thx_in":98.6,"recommended_diagonal_smpte_in":72.6,"recommended_diagonal_range_in":"47–79 in","min_diagonal_for_resolution_in":151.4}

GET https://tttkmbb.com/api/v1/calculate/tv-viewing-distance?diagonal_inches=55&resolution=4k

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/tv-viewing-distance (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/tv-viewing-distance · Markdown: https://tttkmbb.com/everyday/tv-viewing-distance.md · JSON definition: https://tttkmbb.com/everyday/tv-viewing-distance.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="tv-viewing-distance"
OpenAPI operationId: calculate_tv_viewing_distance
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Optimum HDTV viewing distance – THX, SMPTE and visual-acuity limits (Wikipedia) (reference)
RTINGS – TV size to distance calculator and science (reference)

FAQ

Which recommendation should I follow?

For films, THX/SMPTE angles (about 1.2–1.6 × diagonal) give a cinematic field of view; for mixed TV viewing most people sit at 1.5–2.5 × diagonal, which is why that rule persists.

Is 4K worth it at my distance?

Compare your distance with full_resolution_distance_m: beyond it a 20/20 viewer cannot see the extra pixels, though HDR and better processing still improve the picture.

Where does the THX 36° figure come from?

THX certifies cinemas so the back row has at least a 36° view (≈1.34 × diagonal, 1.87 m for a 55-inch screen); the 40° and 28° values here are THX's home-theatre guidance.

Related calculators

Screen PPI Calculator — Pixel density of the same screen.
Projector Throw Distance Calculator — Projector distance for a given image width.
Aspect Ratio Calculator — Screen dimensions from a ratio.