That converter is misleading - it can produce only approximations (or at the very best, results that work for your specific display), but never generally accurate results.
The number of pixels per mm (or any other physical unit) will vary from display to display, as different displays will have a different number of differently sized pixels. See "Pixel Density" in Wikipedia.
You can specify physical measures in CSS and when printing they should come out OK if the browser and the printer driver are handling things right:
.mysheet { width: 19.2cm; height: 8cm; }
Some Browser/OS/display combinations (I don't know which protocols do this) apparently also can interpret physical measures and render them in their correct size on screen.