Screen Size Calculator
Work out a screen's real width and height from its diagonal and aspect ratio, with pixel density in PPI, dot pitch and viewing distance.
How to use this calculator
- 1Enter the advertised diagonal and pick the aspect ratio.
- 2Add the resolution to get pixel density, dot pitch and the distance at which pixels stop being visible.
- 3Compare the table to see how much screen area the same diagonal gives in other shapes.
How the calculation works
width = d × w ÷ √(w² + h²) height = d × h ÷ √(w² + h²) PPI = √(px² + py²) ÷ d dot pitch = 25.4 ÷ PPI- d
- Screen diagonal in inches — the advertised size
- w : h
- Aspect ratio, such as 16:9
- px, py
- Horizontal and vertical resolution in pixels
- PPI
- Pixels per inch, the measure of how sharp the display is
- 25.4
- Millimetres per inch, exactly — the inch is defined as 25.4 mm
The diagonal divides into width and height by similar triangles, not proportionally. A 27-inch 16:9 monitor is 23.53 inches wide and 13.24 tall; nothing about it measures 27 inches except the corner-to-corner line.
This is why screens of the same advertised size differ so much in area. Wider aspect ratios give less area for the same diagonal: a 27" 16:9 panel has 311 in² of screen, but a 27" 32:9 panel has only 179 in².
PPI uses the pixel diagonal over the physical diagonal. That works for any aspect ratio provided the pixels are square, which they are on every modern display.
Dot pitch is simply the reciprocal of PPI converted to millimetres. The inch is defined as exactly 25.4 mm, so the conversion is exact rather than approximate.
Worked example
A 27-inch 1440p monitor
- 1.For 16:9, the ratio diagonal is √(16² + 9²) = √337 = 18.3576.
- 2.Width: 27 × 16 ÷ 18.3576 = 23.53 inches.
- 3.Height: 27 × 9 ÷ 18.3576 = 13.24 inches.
- 4.Check: √(23.53² + 13.24²) = 27 ✓.
- 5.Pixel diagonal: √(2560² + 1440²) = √(6,553,600 + 2,073,600) = 2937.21 px.
- 6.PPI: 2937.21 ÷ 27 = 108.79, and dot pitch is 25.4 ÷ 108.79 = 0.2335 mm.
Result: 23.53" × 13.24", 108.79 PPI
Why a 24-inch 1080p screen looks softer
- 1.Width: 24 × 16 ÷ 18.3576 = 20.92 inches; height 11.77 inches.
- 2.Pixel diagonal: √(1920² + 1080²) = 2202.91 px.
- 3.PPI: 2202.91 ÷ 24 = 91.79 — noticeably below the 27" 1440p panel's 108.79.
- 4.Dot pitch is 0.2767 mm, so pixels are about 18% larger.
- 5.Pixels stay individually visible until roughly 32 inches away, further than most people sit from a monitor.
Result: 20.92" × 11.77", 91.79 PPI
Why the same size screen is not the same amount of screen
Screens are sold by diagonal, which is the one dimension that tells you least about how much screen you get. Two panels advertised at 27 inches can differ by 40% in area depending on their shape, because area falls as the aspect ratio widens for a fixed diagonal.
A 27" 4:3 panel has 350 in² of screen. The same diagonal in 16:9 gives 311 in², in 21:9 gives 268 in², and in 32:9 gives just 179 in² — barely half the 4:3 figure. The ultrawide is not a bigger monitor; it is a differently shaped one with less glass.
This also explains the jump in perceived size when televisions moved from 4:3 to 16:9. A "same size" replacement was in fact a smaller screen, which is part of why screen sizes crept upward through the transition.
Pixel density, and the distance that decides it
PPI on its own says nothing about whether a screen looks sharp. What matters is angular resolution — how much of your field of view a single pixel occupies — and that depends on how far away you sit.
A typical eye resolves detail down to about one arcminute, a sixtieth of a degree. At normal phone distance of 12 inches that works out to roughly 290 PPI, which is why phones cluster in the 400–500 PPI range and gain little from going higher. At a 24-inch desk distance the threshold falls to about 145 PPI; at a 10-foot sofa distance it is around 30 PPI.
That last figure is why 4K matters far less on a television than the marketing suggests. At 10 feet, a 55" 4K set and a 55" 1080p set are both beyond the eye's resolving power for most content — the visible improvements come from contrast, colour and HDR, not pixel count.
Ratios that are not what they claim
Two widely advertised aspect ratios are not the numbers on the box. "21:9" ultrawide panels are actually 64:27, or about 2.370:1 — 21:9 would be 2.333:1. The marketing name was chosen because it reads as a step up from 16:9, and 64:27 is 16:9 multiplied by 4:3, which is how the standard was derived.
The 1366×768 laptop panel is sold as 16:9 but is really 683:384, or 1.7786:1 against 16:9's 1.7778:1. The discrepancy exists because 768 × 16/9 is 1365.33, and panel makers rounded up to an even number. It is close enough to be invisible but means the pixel grid is fractionally non-standard.
These matter mainly when content is scaled: a genuinely 16:9 video on a 683:384 panel is either very slightly stretched or letterboxed by less than a pixel, which no one notices. The lesson is to trust measured pixel dimensions over the marketed ratio name.
What this assumes, and where it stops
Assumptions
- The diagonal is the active display area, which is how monitors and televisions are specified.
- Pixels are square, as they are on every current display technology.
- The visibility distance uses one arcminute of angular resolution, the standard figure for 20/20 vision.
Limitations
- Describes the panel only. Bezels, stand and chassis add to the physical footprint and vary by model.
- Assumes a flat screen. On curved monitors the diagonal is measured along the curve, so the straight-line width is slightly less than calculated.
- PPI measures pixel count per inch, not perceived sharpness. Subpixel layout, anti-aliasing and scaling settings all affect how sharp text actually looks.
- The one-arcminute visibility threshold is a population average. Individual acuity varies considerably.
Common questions
How wide is a 27-inch monitor?
A 27-inch 16:9 monitor is 23.53 inches wide and 13.24 inches tall, or about 59.8 cm by 33.6 cm. The 27 inches refers only to the corner-to-corner diagonal. Add a few centimetres for bezels and the stand when planning desk space.
How do I calculate PPI?
Divide the pixel diagonal by the screen diagonal in inches: PPI = √(width² + height²) ÷ diagonal. For a 27-inch 2560×1440 monitor that is √(2560² + 1440²) ÷ 27 = 2937.21 ÷ 27 = 108.8 PPI.
Is a 27-inch ultrawide bigger than a 27-inch normal monitor?
No — it is smaller in area. For a fixed diagonal, widening the aspect ratio reduces the screen area. A 27" 16:9 panel has about 311 in² of screen, while a 27" 32:9 panel has only 179 in². Ultrawides are usually sold in larger diagonals precisely to compensate.
How much PPI do I actually need?
It depends entirely on viewing distance. At phone distance, around 12 inches, roughly 290 PPI exceeds what a typical eye can resolve. At a 24-inch desk distance about 145 PPI is the threshold, and at a 10-foot sofa distance around 30 PPI. Beyond those figures extra pixels are invisible.
Sources
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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