If you switch a 27-inch monitor from QHD (2560×1440) to 4K (3840×2160), how much smaller does the same text get, and what Windows scaling percentage brings it back to the previous size? With just the screen size and resolution, you can work it out from pixel density (PPI).
PPI is diagonal pixels divided by diagonal inches
PPI (pixels per inch) is the number of pixels in one inch. Monitor sizes are given as diagonal inches, so you first find the diagonal pixel count from the horizontal and vertical pixels, then divide by the inches.
PPI = √(horizontal pixels² + vertical pixels²) ÷ diagonal inches
For a 27-inch QHD screen, √(2560² + 1440²) = 2,937.2 pixels, divided by 27, gives 108.8 PPI. Microsoft's Windows automatic DPI configuration document lists the “Physical DPI” of a 27-inch 2560×1440 monitor as 109 in its sample monitor table. Apple lists the 27-inch 5120×2880 panel as “218 pixels per inch” in the Studio Display technical specifications; the same formula gives 217.6. Manufacturer figures are rounded.
| Screen | Resolution (pixels) | Diagonal pixels | PPI |
|---|---|---|---|
| 27-inch | 2560×1440 | 2,937.2 | 108.8 |
| 27-inch | 3840×2160 | 4,405.8 | 163.2 |
| 27-inch | 5120×2880 | 5,874.4 | 217.6 |
PPI is rounded to one decimal place. The nominal size is used as is, so a product whose visible area is slightly smaller than labeled has a slightly higher PPI.
The actual height of 12-point text
How Windows converts text to pixels is described in Microsoft's DPI and device-independent pixels document. It explains the conversion “One logical inch equals 96 pixels” and, on that basis, calculates that “A 12-point font is 16 pixels tall.” It lists the standard settings as “100% (96 DPI), 125% (120 DPI), and 150% (144 DPI).”
The assumptions: a 27-inch 16:9 monitor, apps that follow the Windows scale setting, and text height taken as the pixel height of a 12-point font (16 pixels at 100%). Physical height (mm) is pixels ÷ PPI × 25.4. Workspace is the effective resolution, the horizontal and vertical pixels divided by the scale.
| Setup | 12pt text pixels | Physical height (mm) | Effective resolution |
|---|---|---|---|
| QHD, 100% scale | 16 | 3.74 | 2560×1440 |
| 4K, 100% scale | 16 | 2.49 | 3840×2160 |
| 4K, 125% scale | 20 | 3.11 | 3072×1728 |
| 4K, 150% scale | 24 | 3.74 | 2560×1440 |
At the same 27 inches, 4K has exactly 1.5 times the PPI of QHD (163.2 ÷ 108.8, the same ratio as 3840 ÷ 2560 horizontal pixels). So at 100%, 4K text shrinks to two-thirds of the QHD height, 2.49 mm, and at 150% it returns to the 3.74 mm of QHD at 100%. The effective resolution also becomes the same 2560×1440. The amount of windows and text that fit on screen matches QHD, while each character is drawn with 1.5 times as many pixels horizontally and vertically, so outlines are denser. 125% sits in between: text is about 17% smaller than QHD at 100%, and the workspace is 1.2 times larger in each direction.
When the calculation does not match
The scale Windows picks at first may differ from this calculation. The automatic DPI configuration document says it selects 100% below 116 physical DPI, 125% for 116 to 138, and 150% above 138, and that physical DPI is calculated from the monitor's EDID data. However, that document keeps a setting deprecated in Windows 8.1 for reference only. It does not confirm how current versions of Windows choose the recommended scale.
Older apps that do not follow the scale setting behave differently. Microsoft's document explains that if a program is not marked as DPI aware, the DWM (Desktop Window Manager) will “scale the entire UI to match the DPI setting.” Because the scaling is applied after the window is drawn, the document notes a somewhat blurry appearance. In such apps the text size matches but sharpness does not rise as much as the table suggests. This calculation answers only the physical size on the screen.