Increasing resolution of large lo res image

 By the way, you are mistaken Sid in referring to DPI as a letterpress screen term, the correct term for the resolution of a half-tone screen is LPI (lines per inch). The rule-of-thumb of suggesting a resolution of 300PPI is that it gives 2 pixels per halftone dot - 150LPI being good halftone screen resolution for letterpress or litho printing on coated substrate. (The term DPI is correctly - though often confused with PPI - used for desktop printer resolution, typically laser printers - nowadays between 600 to 1200DPI.)

"I had a discussion with someone today who said that wouldn't work."

You are correct.  Have your friend pickup a copy of Adobe's Print Publishing Guide.  A great resource for anyone who is having difficulty understanding.  I would love to hear their argument as to why it "wouldn't work".

The dimensions 1000px x 1000px would be the same at 72PPI as 300PPI

The terminology is PPI (Pixels Per Inch) not DPI (Dots Per Inch) – DPI is the resolution term for desk-top printers.

The rule of thumb for raster images to be commercially litho printed is 300PPI which would allow 150 LPI (Lines Per Inch) which is the usual half-tone screen measurement for printing on a coated stock (paper). So an image of 1000 x1000px at 300PPI would print well at around 3.3" x 3.3".

Here's a screen shot to illustrate the point – the top one is the original size at 1000 x 1000 px at a resolution of 72PPI (if you're using the image for the web, and similar screen use, the resolution is irrelevant). In the bottom screen shot, the image in Photoshop: Image > Image Size – Resample is unticked and the new resolution of 300PPI has been entered.

Note the new printing size of 3.3" x 3.3" but the overall dimensions are still 1000 x 1000px.

(Click on the images to see them enlarged.)

You are on the right lines but incorrect in that you are changing the number of pixels in your example.

The document resolution ppi is just a number stored separately to the pixels. It is used to calculate a physical size. To leave the document unchanged and just change the ppi and hence the size of print in inches or centimetres use Image >Image Size but leave resample unchecked.

1000 x 1000 pixels at 72 ppi measures 13.88 x 13.88 inches.

1000 x 1000 pixels at 300ppi measures 3.33 x 3.33 inches but contains exactly the same picture information because the picture information is in the pixel size (which is unchanged)  not the ppi value.

If you resample and change to 250 x 250 pixels at 300ppi then it measures 0.83 x 0.83 inches but you have thrown away pixels. Instead of 1,000,000 pixels you now have 62,500 pixels so you have thrown away 93% of the original and will have severe degradation of the image.

Dave