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Screen PPI Calculator

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.

When to use

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).

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°)

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.

Inputs

Parameter	Type	Unit	Required	Description
`diagonal_inches`	number	in	yes	Screen diagonal in inches (the advertised size). Range: > 0, ≤ 500
`width_px`	integer	px	yes	Pixels across. Range: ≥ 1, ≤ 100000
`height_px`	integer	px	yes	Pixels down. Range: ≥ 1, ≤ 100000

Outputs

Output	Type	Unit	Description
`ppi`	number	ppi	√(width_px² + height_px²) / diagonal_inches.
`ppcm`	number	px/cm	ppi / 2.54.
`dot_pitch_mm`	number	mm	Centre-to-centre pixel spacing = 25.4 / ppi.
`aspect_ratio`	string		Simplified width:height.
`total_pixels`	integer	px	width_px × height_px.
`megapixels`	number	MP	total_pixels / 10⁶.
`screen_width_cm`	number	cm	Active-area width = width_px / ppi × 2.54.
`screen_height_cm`	number	cm	Active-area height.
`screen_width_in`	number	in	Width in inches.
`screen_height_in`	number	in	Height in inches.
`retina_distance_cm`	number	cm	Viewing distance beyond which one pixel subtends less than 1 arcminute (20/20 acuity): dot_pitch / tan(1′).

Example

27-inch 2560 × 1440 monitor: {"diagonal_inches":27,"width_px":2560,"height_px":1440} → {"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}

15.6-inch 1920 × 1080 laptop: {"diagonal_inches":15.6,"width_px":1920,"height_px":1080} → {"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}

GET https://tttkmbb.com/api/v1/calculate/screen-ppi?diagonal_inches=27&width_px=2560&height_px=1440

Machine access

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

Sources

Pixel density (Wikipedia) (reference)
Visual acuity – the 1 arcminute standard (Wikipedia) (reference)

FAQ

What PPI counts as sharp?

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.

Why does my 1366 × 768 screen show 683:384?

That is the exact reduced ratio; it is only approximately 16:9. Use aspect-ratio for the closest common ratio.

Related calculators

TV Viewing Distance Calculator — How far to sit from a screen of this size and resolution.
Aspect Ratio Calculator — Closest standard aspect ratio and resizing.
Pythagorean Theorem Calculator — The diagonal-pixel calculation is the Pythagorean theorem.