ok, for 300 dpi one cm is 118 pixels.

You simply can do that calculation in a  program like Photoshop - define a new image with A4 size and with 300 dpi and see how many pixels there are.

Btw - in terms of quality you could live as well with 225 dpi as well. This is the mathematical solution of the equation (223.6 to be precise). 300 is only a security distance value.

One day your ship comes in - but you're at the airport.