I have an approximately 2500 pixel x 3500 pixel image. How do I figure out the largest print that I can get from it? At the 300 dpi printing standard that would only yield about 8x12" but I need something larger. Larger than A4.
Do the math. If you really need 300 DPI, then at most your picture can be (2500 pixels)/(300 pixels/inch) = 8.3 inches wide.
If you want bigger than that you either can't, or you have to relax your resolution requirements. 200 DPI might still be good enough for something hand-held, for example.
The resolution the picture needs to have depends on viewing distance. Let's say you've decided that 200 DPI is sufficient when viewed from 18 inches. The minimum DPI you need is inversely proportional to distance. If the print will be viewed from 6 feet away, for example, then it only needs to be printed at 50 DPI, which means it can be 50 inches wide.
Conversely, if the picture is for a billboard 20 feet wide, then you only get 10.4 DPI, and the viewer has to be 29 feet back to have it look like the 200 DPI print at 18 inches.