PPI calculator
A 27-inch 1440p monitor at 109 PPI looks sharp at arm length and coarse if you lean in. A phone at 460 PPI looks sharp at 30 cm and would look coarse held to your nose. What actually determines whether pixels are visible is angular resolution — the eye resolves about one arcminute, so the required density falls linearly with viewing distance. A billboard at 10 PPI is perfectly sharp from the road.
Pixel density is the diagonal pixel count divided by the diagonal in inches. A 27-inch 2560×1440 monitor works out at 108.79 PPI, with a dot pitch of 0.2335 mm and a physical panel 59.7 cm wide.
How to calculate PPI
Around 110 PPI is the comfortable zone for a desktop monitor at normal viewing distance, which is why 24-inch 1080p and 27-inch 1440p both feel similar and why 27-inch 1080p at 82 PPI looks noticeably soft. Above about 150 PPI, operating systems generally need fractional scaling to keep interface elements a usable size, and how well that is handled varies considerably between platforms — which is a practical argument for choosing a density that lands near a clean 100% or 200% rather than at 150.
Questions
Around 110 for a desktop at arm length. 24-inch 1080p and 27-inch 1440p both land close to it.