Whether your image has enough pixels for the size you are printing it, judged against the actual halftone screen, not a blanket 300 dpi rule.
300 ppi is not a constant. It is two times 150 lpi
A press cannot print a continuous tone, so it breaks the image into a grid of dots of varying size — a halftone screen, measured in lines per inch. ISO 12647-2 specifies 48 to 80 lines per centimetre for four-colour offset, which is 120 to 200 lpi. The middle of that range is about 150.
The relationship between image resolution and screen ruling is the quality factor, and Adobe ships it as a feature: Photoshop's Auto Resolution dialog offers Draft at 1× the screen ruling, Good at 1.5× and Best at 2×. Two times 150 lpi is 300 ppi. That is the entire derivation.
Which means 300 is the right answer for one specific screen ruling and the wrong answer for others. A newspaper at around 100 lpi needs 200 ppi. An art book at 200 lpi wants 400. Not one page-one search result for any resolution query explains this, and the one site that cites a standard for it miscites the standard.
Above 2.5 times the screen ruling, nothing improves
Photoshop raises a warning if you print an image at more than 2.5 times the screen ruling, and the wording is unambiguous: the resolution is higher than the printer needs. The extra pixels cost file size and processing time and change nothing on the sheet.
Printers act on this. PrintNinja caps submitted files at 400 dpi and says so plainly; Mixam gives the same figure. If someone has told you to send 600 dpi photographs, they are thinking of line art, which is a genuinely different case — one-bit black and white does want 600 to 1200 dpi, because there is no halftone cell to hide the staircase.
Effective resolution is what preflight actually checks
The resolution stored in a file is a label. What matters is the resolution at the size it is placed, which is the native figure divided by the scale factor. A 300 ppi image scaled to 200 per cent in a layout is a 150 ppi image.
InDesign shows both numbers side by side and calls them Actual PPI and Effective PPI. It is the effective one that a preflight profile tests and the effective one that determines what comes off the press. A file can be tagged 300 ppi, pass a naive check, and print soft.
Resampling up does not add detail
Changing the resolution field from 72 to 300 with resampling switched on does not create information. It interpolates — it invents new pixels by averaging the ones around them. The file will report 300 ppi and print exactly as soft as it did before.
Adobe's own guidance is blunt: to produce a larger image, rescan at a higher resolution. The one genuine improvement is machine-learning upscaling, which guesses from a trained prior rather than from neighbouring pixels and produces markedly better edges. It is still inference rather than capture, and Adobe scopes its own claim carefully — two times the linear resolution, aimed at large prints and cropped images.
The correct move when a file is high-resolution but tagged 72 ppi is to switch resampling OFF and then change the resolution. The pixel count stays put and only the print size changes, which is what you wanted.
Asked often
Is 300 dpi always right?
No. It is 2 × 150 lpi, and 150 lpi is one point in the range ISO 12647-2 allows. Newsprint at around 100 lpi needs 200 ppi; a fine art book at 200 lpi wants 400.
Can I just increase the resolution in Photoshop?
Not with resampling on — that invents pixels and the print stays soft. With resampling off, changing the resolution only changes the print size, which is usually what you actually want.
What resolution does a billboard need?
Far less than people expect. Lamar's bulletin specs work out at about 12.5 ppi at final size. Viewing distance is the variable, not the medium.