{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"screen-ppi"},"result":{"entity_type":"calculator","id":"screen-ppi","calculator_id":"screen-ppi","canonical_url":"https://tttkmbb.com/everyday/screen-ppi","name":"Screen PPI Calculator","title":"Screen PPI Calculator – Pixel Density, Dot Pitch, Aspect Ratio and Physical Size from Diagonal and Resolution","category":"everyday","category_name":"Everyday Life","tool_name":"calculate_screen_ppi","featured_mcp_tool":false,"description":"Computes pixels per inch and per centimetre, dot pitch, total pixels, the simplified aspect ratio and the physical width and height of a display from its diagonal size and pixel resolution, plus the distance beyond which 20/20 vision can no longer resolve individual pixels.","use_when":"You are comparing monitors, phones or TVs by sharpness, need the physical width of a screen, or want to know at what distance a display looks 'retina'.","do_not_use_when":"You need viewing-distance recommendations for a TV (use tv-viewing-distance) or only the aspect ratio (use aspect-ratio).","inputs":[{"name":"diagonal_inches","label":"Diagonal size","type":"number","unit":"in","required":true,"max":500,"exclusive_min":0,"description":"Screen diagonal in inches (the advertised size).","example":27},{"name":"width_px","label":"Horizontal resolution","type":"integer","unit":"px","required":true,"min":1,"max":100000,"description":"Pixels across.","example":2560},{"name":"height_px","label":"Vertical resolution","type":"integer","unit":"px","required":true,"min":1,"max":100000,"description":"Pixels down.","example":1440}],"outputs":[{"name":"ppi","label":"Pixel density","type":"number","unit":"ppi","decimals":2,"description":"√(width_px² + height_px²) / diagonal_inches."},{"name":"ppcm","label":"Pixel density","type":"number","unit":"px/cm","decimals":2,"description":"ppi / 2.54."},{"name":"dot_pitch_mm","label":"Dot pitch","type":"number","unit":"mm","decimals":4,"description":"Centre-to-centre pixel spacing = 25.4 / ppi."},{"name":"aspect_ratio","label":"Aspect ratio","type":"string","decimals":4,"description":"Simplified width:height."},{"name":"total_pixels","label":"Total pixels","type":"integer","unit":"px","decimals":4,"description":"width_px × height_px."},{"name":"megapixels","label":"Megapixels","type":"number","unit":"MP","decimals":2,"description":"total_pixels / 10⁶."},{"name":"screen_width_cm","label":"Screen width","type":"number","unit":"cm","decimals":2,"description":"Active-area width = width_px / ppi × 2.54."},{"name":"screen_height_cm","label":"Screen height","type":"number","unit":"cm","decimals":2,"description":"Active-area height."},{"name":"screen_width_in","label":"Screen width","type":"number","unit":"in","decimals":2,"description":"Width in inches."},{"name":"screen_height_in","label":"Screen height","type":"number","unit":"in","decimals":2,"description":"Height in inches."},{"name":"retina_distance_cm","label":"Pixel-invisible distance","type":"number","unit":"cm","decimals":1,"description":"Viewing distance beyond which one pixel subtends less than 1 arcminute (20/20 acuity): dot_pitch / tan(1′)."}],"input_schema":{"type":"object","properties":{"diagonal_inches":{"description":"Screen diagonal in inches (the advertised size). Unit: in.","type":"number","maximum":500,"exclusiveMinimum":0,"examples":[27],"x-unit":"in"},"width_px":{"description":"Pixels across. Unit: px.","type":"integer","minimum":1,"maximum":100000,"examples":[2560],"x-unit":"px"},"height_px":{"description":"Pixels down. Unit: px.","type":"integer","minimum":1,"maximum":100000,"examples":[1440],"x-unit":"px"}},"additionalProperties":false,"required":["diagonal_inches","width_px","height_px"]},"output_schema":{"type":"object","properties":{"ppi":{"description":"√(width_px² + height_px²) / diagonal_inches. Unit: ppi.","type":"number","x-unit":"ppi"},"ppcm":{"description":"ppi / 2.54. Unit: px/cm.","type":"number","x-unit":"px/cm"},"dot_pitch_mm":{"description":"Centre-to-centre pixel spacing = 25.4 / ppi. Unit: mm.","type":"number","x-unit":"mm"},"aspect_ratio":{"description":"Simplified width:height.","type":"string"},"total_pixels":{"description":"width_px × height_px. Unit: px.","type":"integer","x-unit":"px"},"megapixels":{"description":"total_pixels / 10⁶. Unit: MP.","type":"number","x-unit":"MP"},"screen_width_cm":{"description":"Active-area width = width_px / ppi × 2.54. Unit: cm.","type":"number","x-unit":"cm"},"screen_height_cm":{"description":"Active-area height. Unit: cm.","type":"number","x-unit":"cm"},"screen_width_in":{"description":"Width in inches. Unit: in.","type":"number","x-unit":"in"},"screen_height_in":{"description":"Height in inches. Unit: in.","type":"number","x-unit":"in"},"retina_distance_cm":{"description":"Viewing distance beyond which one pixel subtends less than 1 arcminute (20/20 acuity): dot_pitch / tan(1′). Unit: cm.","type":"number","x-unit":"cm"}}},"formula":"ppi = √(width_px² + height_px²) / diagonal_inches; dot_pitch_mm = 25.4 / ppi; width_in = width_px / ppi; height_in = height_px / ppi; aspect = width_px : height_px reduced by their gcd; retina_distance = dot_pitch / tan(1/60°)","method":"Assumes square pixels and that the quoted diagonal is the active area (manufacturers round it, e.g. a 6.1-inch phone panel gives ~457 ppi here versus the advertised 460). The 1-arcminute criterion is the classic 20/20 limit; people with sharper vision resolve about 0.6 arcminutes.","sources":[{"name":"Pixel density (Wikipedia)","url":"https://en.wikipedia.org/wiki/Pixel_density","type":"reference","retrieved_at":"2026-09-24"},{"name":"Visual acuity – the 1 arcminute standard (Wikipedia)","url":"https://en.wikipedia.org/wiki/Visual_acuity","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":"27-inch 2560 × 1440 monitor","inputs":{"diagonal_inches":27,"width_px":2560,"height_px":1440},"expected":{"ppi":108.79,"ppcm":42.83,"dot_pitch_mm":0.2335,"aspect_ratio":"16:9","total_pixels":3686400,"megapixels":3.69,"screen_width_cm":59.77,"screen_height_cm":33.62,"screen_width_in":23.53,"screen_height_in":13.24,"retina_distance_cm":80.3},"url":"https://tttkmbb.com/api/v1/calculate/screen-ppi?diagonal_inches=27&width_px=2560&height_px=1440"},{"name":"15.6-inch 1920 × 1080 laptop","inputs":{"diagonal_inches":15.6,"width_px":1920,"height_px":1080},"expected":{"ppi":141.21,"dot_pitch_mm":0.1799,"aspect_ratio":"16:9","total_pixels":2073600,"screen_width_cm":34.54,"screen_height_cm":19.43,"retina_distance_cm":61.8},"url":"https://tttkmbb.com/api/v1/calculate/screen-ppi?diagonal_inches=15.6&width_px=1920&height_px=1080"}],"faq":[{"q":"What PPI counts as sharp?","a":"It depends on distance: at 60 cm a monitor needs about 145 ppi to hide pixels for 20/20 vision, a phone at 30 cm about 290 ppi, and a TV at 2.5 m only about 35 ppi."},{"q":"Why does my 1366 × 768 screen show 683:384?","a":"That is the exact reduced ratio; it is only approximately 16:9. Use aspect-ratio for the closest common ratio."}],"tags":["ppi calculator","pixel density","dots per inch screen","dot pitch","monitor size calculator"],"related":[{"calculator_id":"tv-viewing-distance","reason":"How far to sit from a screen of this size and resolution."},{"calculator_id":"aspect-ratio","reason":"Closest standard aspect ratio and resizing."},{"calculator_id":"pythagorean","reason":"The diagonal-pixel calculation is the Pythagorean theorem."}],"links":{"html":"https://tttkmbb.com/everyday/screen-ppi","markdown":"https://tttkmbb.com/everyday/screen-ppi.md","json":"https://tttkmbb.com/everyday/screen-ppi.json","api":"https://tttkmbb.com/api/v1/calculate/screen-ppi","schema":"https://tttkmbb.com/api/v1/calculators/screen-ppi","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:57:59Z"}