{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"tv-viewing-distance"},"result":{"entity_type":"calculator","id":"tv-viewing-distance","calculator_id":"tv-viewing-distance","canonical_url":"https://tttkmbb.com/everyday/tv-viewing-distance","name":"TV Viewing Distance Calculator","title":"TV Viewing Distance Calculator – THX 40°, SMPTE 30°, 1.5–2.5× Rule and 4K/1080p Resolution Distances","category":"everyday","category_name":"Everyday Life","tool_name":"calculate_tv_viewing_distance","featured_mcp_tool":false,"description":"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.","inputs":[{"name":"diagonal_inches","label":"Screen diagonal","type":"number","unit":"in","required":false,"max":500,"exclusive_min":0,"description":"TV diagonal in inches. Give this and/or viewing_distance_m.","example":55},{"name":"viewing_distance_m","label":"Viewing distance","type":"number","unit":"m","required":false,"max":50,"exclusive_min":0,"description":"Eye-to-screen distance in metres. Given alone, screen sizes are recommended; with the diagonal, the actual viewing angle is reported.","example":3},{"name":"resolution","label":"Resolution","type":"enum","required":false,"default":"4k","values":[{"value":"1080p","label":"1080p (1920 px wide)","aliases":["full hd","fhd"]},{"value":"4k","label":"4K UHD (3840 px wide)","aliases":["2160p","uhd"]},{"value":"8k","label":"8K (7680 px wide)","aliases":["4320p"]}],"description":"Panel resolution used for the full-detail distance.","example":"4k"},{"name":"aspect_ratio","label":"Aspect ratio","type":"enum","required":false,"default":"16:9","values":[{"value":"16:9","label":"16:9 (HDTV, most projectors)","aliases":["16x9","1.78:1"]},{"value":"21:9","label":"21:9 ultrawide","aliases":["ultrawide"]},{"value":"4:3","label":"4:3","aliases":["1.33:1"]}],"description":"Width-to-height ratio of the screen or image.","example":"16:9"}],"outputs":[{"name":"screen_width_cm","label":"Screen width","type":"number","unit":"cm","decimals":1,"description":"Width of the picture (diagonal mode)."},{"name":"screen_height_cm","label":"Screen height","type":"number","unit":"cm","decimals":1,"description":"Height of the picture (diagonal mode)."},{"name":"thx_40deg_m","label":"THX best seat (40°)","type":"number","unit":"m","decimals":2,"description":"Distance at which the screen spans 40° = width / (2 × tan 20°) ≈ 1.2 × diagonal."},{"name":"thx_28deg_m","label":"THX maximum (28°)","type":"number","unit":"m","decimals":2,"description":"Farthest THX-recommended seat, 28° ≈ 1.75 × diagonal."},{"name":"smpte_30deg_m","label":"SMPTE (30°)","type":"number","unit":"m","decimals":2,"description":"Distance for a 30° field of view ≈ 1.63 × diagonal."},{"name":"rule_min_m","label":"1.5 × diagonal","type":"number","unit":"m","decimals":2,"description":"Near end of the popular 1.5–2.5× diagonal range."},{"name":"rule_max_m","label":"2.5 × diagonal","type":"number","unit":"m","decimals":2,"description":"Far end of the 1.5–2.5× range."},{"name":"full_resolution_distance_m","label":"Full-resolution distance","type":"number","unit":"m","decimals":2,"description":"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."},{"name":"viewing_angle_deg","label":"Actual viewing angle","type":"number","unit":"°","decimals":1,"description":"Horizontal angle the screen subtends at viewing_distance_m (only when both inputs are given)."},{"name":"recommended_diagonal_thx_in","label":"Diagonal for THX 40°","type":"number","unit":"in","decimals":1,"description":"Screen size that spans 40° at viewing_distance_m (distance mode)."},{"name":"recommended_diagonal_smpte_in","label":"Diagonal for SMPTE 30°","type":"number","unit":"in","decimals":1,"description":"Screen size that spans 30° at viewing_distance_m."},{"name":"recommended_diagonal_range_in","label":"Diagonal by 1.5–2.5× rule","type":"string","decimals":4,"description":"Range of sizes for which the distance is 1.5–2.5 diagonals."},{"name":"min_diagonal_for_resolution_in","label":"Smallest size to see full resolution","type":"number","unit":"in","decimals":1,"description":"Diagonal at which the chosen resolution is just fully resolved from viewing_distance_m."}],"input_schema":{"type":"object","properties":{"diagonal_inches":{"description":"TV diagonal in inches. Give this and/or viewing_distance_m. Unit: in.","type":"number","maximum":500,"exclusiveMinimum":0,"examples":[55],"x-unit":"in"},"viewing_distance_m":{"description":"Eye-to-screen distance in metres. Given alone, screen sizes are recommended; with the diagonal, the actual viewing angle is reported. Unit: m.","type":"number","maximum":50,"exclusiveMinimum":0,"examples":[3],"x-unit":"m"},"resolution":{"description":"Panel resolution used for the full-detail distance.","type":"string","enum":["1080p","4k","8k"],"default":"4k","examples":["4k"]},"aspect_ratio":{"description":"Width-to-height ratio of the screen or image.","type":"string","enum":["16:9","21:9","4:3"],"default":"16:9","examples":["16:9"]}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"screen_width_cm":{"description":"Width of the picture (diagonal mode). Unit: cm.","type":"number","x-unit":"cm"},"screen_height_cm":{"description":"Height of the picture (diagonal mode). Unit: cm.","type":"number","x-unit":"cm"},"thx_40deg_m":{"description":"Distance at which the screen spans 40° = width / (2 × tan 20°) ≈ 1.2 × diagonal. Unit: m.","type":"number","x-unit":"m"},"thx_28deg_m":{"description":"Farthest THX-recommended seat, 28° ≈ 1.75 × diagonal. Unit: m.","type":"number","x-unit":"m"},"smpte_30deg_m":{"description":"Distance for a 30° field of view ≈ 1.63 × diagonal. Unit: m.","type":"number","x-unit":"m"},"rule_min_m":{"description":"Near end of the popular 1.5–2.5× diagonal range. Unit: m.","type":"number","x-unit":"m"},"rule_max_m":{"description":"Far end of the 1.5–2.5× range. Unit: m.","type":"number","x-unit":"m"},"full_resolution_distance_m":{"description":"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. Unit: m.","type":"number","x-unit":"m"},"viewing_angle_deg":{"description":"Horizontal angle the screen subtends at viewing_distance_m (only when both inputs are given). Unit: °.","type":"number","x-unit":"°"},"recommended_diagonal_thx_in":{"description":"Screen size that spans 40° at viewing_distance_m (distance mode). Unit: in.","type":"number","x-unit":"in"},"recommended_diagonal_smpte_in":{"description":"Screen size that spans 30° at viewing_distance_m. Unit: in.","type":"number","x-unit":"in"},"recommended_diagonal_range_in":{"description":"Range of sizes for which the distance is 1.5–2.5 diagonals.","type":"string"},"min_diagonal_for_resolution_in":{"description":"Diagonal at which the chosen resolution is just fully resolved from viewing_distance_m. Unit: in.","type":"number","x-unit":"in"}}},"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","method":"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.","sources":[{"name":"Optimum HDTV viewing distance – THX, SMPTE and visual-acuity limits (Wikipedia)","url":"https://en.wikipedia.org/wiki/Optimum_HDTV_viewing_distance","type":"reference","retrieved_at":"2026-09-24"},{"name":"RTINGS – TV size to distance calculator and science","url":"https://www.rtings.com/tv/reviews/by-size/size-to-distance-relationship","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"55-inch 4K TV","inputs":{"diagonal_inches":55,"resolution":"4k"},"expected":{"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},"url":"https://tttkmbb.com/api/v1/calculate/tv-viewing-distance?diagonal_inches=55&resolution=4k"},{"name":"Sofa 3 m from the wall, 4K","inputs":{"viewing_distance_m":3,"resolution":"4k"},"expected":{"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},"url":"https://tttkmbb.com/api/v1/calculate/tv-viewing-distance?viewing_distance_m=3&resolution=4k"}],"faq":[{"q":"Which recommendation should I follow?","a":"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."},{"q":"Is 4K worth it at my distance?","a":"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."},{"q":"Where does the THX 36° figure come from?","a":"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."}],"tags":["tv viewing distance","how far to sit from tv","what size tv for my room","thx viewing distance","4k viewing distance"],"related":[{"calculator_id":"screen-ppi","reason":"Pixel density of the same screen."},{"calculator_id":"projector-throw","reason":"Projector distance for a given image width."},{"calculator_id":"aspect-ratio","reason":"Screen dimensions from a ratio."}],"links":{"html":"https://tttkmbb.com/everyday/tv-viewing-distance","markdown":"https://tttkmbb.com/everyday/tv-viewing-distance.md","json":"https://tttkmbb.com/everyday/tv-viewing-distance.json","api":"https://tttkmbb.com/api/v1/calculate/tv-viewing-distance","schema":"https://tttkmbb.com/api/v1/calculators/tv-viewing-distance","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:48:19Z"}