According to a common misconception, the maximum printed size of a digital image is determined almost entirely by the image file's pixel dimensions, and optimal image quality requires 300 pixels per inch of printed distance in the horizontal or vertical dimension. This is an oversimplification, and it is also inaccurate. Various factors influence the relationship between image file and print size. Pixel count is undoubtedly important, but we must also consider image quality and viewing distance.
An image that suffers from imperfect focus, exposure errors, numerous small defects, distracting distortion, or excessive noise will not be successful as a large print, even if it contains a superabundance of pixels. Image quality is not determined solely by pixel count; rather, pixel count is one parameter that can contribute to image quality.
Photographs of exceptional quality can be printed much larger than some people might expect, because an image file usually does not need to supply 300 pixels per printed inch. Even if we assume that an inkjet printer or optical printing system can faithfully reproduce 300 ppi of detail, the human eye cannot discern this much detail except perhaps at very close viewing distances. Larger prints have fewer pixels per inch, but since we view them from farther away, print quality is not noticeably affected. This relationship has practical limits, though, because we probably don't want to decorate our homes and offices with prints that look good from six feet away but become visually unbearable upon close inspection.
It is not possible to calculate the exact "maximum print size" for any digital image—there are simply too many variables. Most of my fine art photographs will provide excellent quality at print sizes up to 30"×30", 30"×40", or 30"×45" (depending on the aspect ratio of the picture). One of my portraits printed at 30"×45" is currently hanging in my bedroom; it looks absolutely wonderful from normal viewing distances and is not noticeably affected by pixelation or unpleasant artifacts when I examine it from the closest distance at which my eyes can focus. Larger print sizes are certainly possible, but viewing conditions must be taken into account.
If you have any questions about print sizes for particular images, please contact me. I will be happy to discuss any issues related to printing, mounting, and framing.