DPI calculator
Three hundred dots per inch is the standard for anything held in the hand, because that is roughly what the eye resolves at reading distance. A poster viewed from two metres is perfectly sharp at 150 DPI, and a billboard at 20 metres is fine at 15. Printing a billboard at 300 DPI would mean a file of several gigabytes to no visible benefit — which is why large-format printers publish their own distance-based tables.
Print size is pixels divided by DPI. A 3000×2400 image at 300 DPI prints 10 × 8 inches. Going the other way, an 8-inch print at 300 DPI needs 2,400 pixels along that edge.
How to use DPI for printing
DPI is not stored in the pixels — it is a tag, and changing it in software does not add detail. Setting a 1000-pixel image from 72 DPI to 300 DPI without resampling simply declares that it should print smaller. The only ways to genuinely gain print size are to capture at higher resolution or to accept a lower DPI. Upscaling software can invent plausible detail and increasingly does it well, but it is invention rather than recovery.
Questions
Multiply the print dimension in inches by 300. An 8 × 10 print needs 2400 × 3000 pixels.