4×6 in dots, by density
The arithmetic is direct: multiply inches by the density in dots per inch. At 203 dpi, 4 × 203 is 812 dots and 6 × 203 is 1218. Hence ^PW812 and ^LL1218.
The confusing part is that the American 4×6 and the metric 10×15 cm are sold as the same stock, and they are not: 4 inches is 101.6 mm, not 100. At 203 dpi that is 812×1218 against 800×1200 — twelve dots, about 1.5 mm, and enough for a field sitting against the edge to run off.
- 4×6 in — 812×1218 at 203 dpi · 1200×1800 at 300 dpi · 2400×3600 at 600 dpi
- 10×15 cm — 800×1200 at 203 dpi · 1200×1800 at 300 dpi · 2400×3600 at 600 dpi
- 4×2 in — 812×406 at 203 dpi · 1200×600 at 300 dpi
- 2×1 in — 406×203 at 203 dpi · 600×300 at 300 dpi
- At 300 and 600 dpi the first two coincide, because the marketed “300 dpi” is a rounding of 304.8.
^PW and ^LL, and what happens without them
^PW sets the width in dots and ^LL the length. Both apply to the whole label and sit just after ^XA, with the other globally-scoped commands. A field positioned beyond those values is drawn outside the label's area — it exists in the file and never reaches the stock.
Plenty of carrier files carry neither, and that is normal: the printer uses the size already configured on it. Here, with no ^PW and ^LL the canvas grows to fit the graphics rather than cropping — which is why a carrier label often opens at something like 816 dots wide, a width its content asked for rather than one the file declared.
When the size does not match
If the label opened at the wrong size but the artwork is in proportion, the problem is density rather than ^PW: the same 812 dots are 4 inches at 203 dpi and 2.7 at 300. Changing the selector fixes it without touching the file.
If the artwork is clipped on one side only, then it is ^PW or ^LL being smaller than the content. And if the printed label came out smaller than the screen showed, the suspect is the print dialog's “fit to page” — the PDF from here is already at true physical size, so printing at 100% scale is what preserves it.