Pixels and print size
A pixel has no physical size until you decide how tightly the pixels are packed. Everything else follows from that.
A pixel is not a length
Asking how many centimetres a pixel is like asking how many centimetres a word is. A pixel is a unit of image data — one sample of colour. It only acquires a physical size when you decide how many of them fill an inch.
That decision is the density, measured in pixels per inch. At 96 PPI a 1000-pixel width covers about 26.5 cm. At 300 PPI the same 1000 pixels cover about 8.5 cm. Same file, same pixels, very different prints.
Why some tools quietly assume 72 or 96
Older conversion tools default to 72 PPI, a legacy desktop-publishing convention, or 96 PPI, the reference density CSS uses to define an inch. Neither describes your screen or your printer. An answer built on an unstated assumption looks authoritative and is usually wrong, which is why theconverter here asks for a density instead of inventing one.
The two directions
Everything in this cluster comes from one relationship, read in either direction:
inchesequalspixels ÷ PPI
pixelsequalsinches × PPI
Read left to right you are asking how large will this print? — thePrint Size Calculator. Read right to left you are askinghow many pixels do I need? — theRequired Resolution Calculator. They are inverses of each other.
The one deliberate difference
Required Resolution rounds pixel counts up, while ordinary conversions round to the nearest pixel. Rounding down would leave the print fractionally below the density you asked for, so rounding up guarantees the target is met or exceeded. It is the only place on the site where rounding is deliberately one-directional.
Worked example: an A4 print
A4 is 210 × 297 mm, defined by ISO 216. Converted at exactly 25.4 mm to the inch, that is 8.268 × 11.693 inches. At 300 PPI:
widthequals8.268 × 300 = 2480.3 → 2481 px
heightequals11.693 × 300 = 3507.9 → 3508 px
That is roughly 8.7 megapixels — comfortably within reach of most modern cameras.
Choosing a density
300 PPI is a widely used working value for photographic prints held at reading distance, and it is the starting value in the print tools here. It is not a law. Large prints viewed from several metres away are routinely produced at 150 PPI or lower, because the eye cannot resolve the difference at that distance.
Ratio & Rule does not tell you whether a print will look good. That depends on the sharpness of the original, the printer, the paper and the viewing distance — none of which a calculator can see.