# 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.

- Calculator id: `tv-viewing-distance` · Category: Everyday Life (`everyday`) · Tool name: `calculate_tv_viewing_distance`
- Canonical page: https://tttkmbb.com/everyday/tv-viewing-distance · This document: https://tttkmbb.com/everyday/tv-viewing-distance.md · JSON definition: https://tttkmbb.com/everyday/tv-viewing-distance.json

## Purpose

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.

**Use when:** 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.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `diagonal_inches` | number | in | optional | TV diagonal in inches. Give this and/or viewing_distance_m. (> 0, max 500) |
| `viewing_distance_m` | number | m | optional | Eye-to-screen distance in metres. Given alone, screen sizes are recommended; with the diagonal, the actual viewing angle is reported. (> 0, max 50) |
| `resolution` | enum: 1080p \| 4k \| 8k |  | optional, default "4k" | Panel resolution used for the full-detail distance. |
| `aspect_ratio` | enum: 16:9 \| 21:9 \| 4:3 |  | optional, default "16:9" | Width-to-height ratio of the screen or image. |

## Output

| Field | 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. |

## 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.

## Data Sources

- Optimum HDTV viewing distance – THX, SMPTE and visual-acuity limits (Wikipedia) — https://en.wikipedia.org/wiki/Optimum_HDTV_viewing_distance (reference, retrieved 2026-09-24)
- RTINGS – TV size to distance calculator and science — https://www.rtings.com/tv/reviews/by-size/size-to-distance-relationship (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/tv-viewing-distance?`
- `POST https://tttkmbb.com/api/v1/calculate/tv-viewing-distance` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/tv-viewing-distance · OpenAPI operationId `calculate_tv_viewing_distance` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "tv-viewing-distance", "inputs": {…}}`

## Example

- 55-inch 4K TV: inputs `{"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: inputs `{"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
```

## Limitations

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. 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. All values are computed from the formula above; no measurement or live data is involved.

## 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

- [Screen PPI Calculator](https://tttkmbb.com/everyday/screen-ppi.md) — Pixel density of the same screen.
- [Projector Throw Distance Calculator](https://tttkmbb.com/everyday/projector-throw.md) — Projector distance for a given image width.
- [Aspect Ratio Calculator](https://tttkmbb.com/everyday/aspect-ratio.md) — Screen dimensions from a ratio.