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A Collage I am working on will be 48" X 72". I was planning to make 24 X 24 collages and stitch them together. Based on software limitations, my maximum size is 5120 X 5120 Pixels. That would give me about 213ppi for a 24 X 24 print.

I am going to get this printed on glossy sheet paper. Does it make sense to use 213ppi, or should I use some round number like 200 instead?

300 is possible but a bit more work. I have to make more small collages and stitch them.

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Question to consider: do you think it should be a round number in pixels per inch, or in pixels per millimeter? If ppi, why ppi rather than ppm? If you get it round in one unit, it won't be round in another - this is a big clue that it doesn't matter, unless as AJ Henderson says, your printer has a native resolution. –  Philip Kendall Jan 6 at 16:09

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300 would hold up better if people will view it up close, but then again, for up close viewing, chances are the tiles are going to be more visible. If the ideal viewing distance is a bit further away, anything upwards of 150 is fine, though the higher quality you can pull off, the better, so I'd go with 200PPI if you have a native resolution of 600PPI. If you need to find the native resolution of your camera, you can find it with the tool JRista mentions in his answer to this question.

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This big answer on printing includes a section on printer native resolution, and suggests that Choosing a resolution that evenly divides into the native printer resolution, such as 360ppi for Epson, or 300ppi for Canon, will help ensure that any scaling the driver does will produce even results. That's a from 2.5 years ago; have things changed significantly? It sounds like they have — is it now normal for dot size to be effectively infinitely variable, and the optimal size selected automatically? –  mattdm Jan 6 at 21:27
    
I can buy that. It seems less confusing to say "the resolution is so high on modern printers that it's a non issue" than it is to say that there is no resolution, though. Maybe that's just me. –  mattdm Jan 6 at 21:37
    
Works for me. By the way, I'm not playing dumb or anything here: this is an area I really don't know much about. –  mattdm Jan 6 at 21:47
    
300 would hold up better if people will view it up close, but then again, for up close viewing, chances are the tiles are going to be more visible. Could you define distances? –  BBking Jan 13 at 23:49
    
@BBking - it really depends on the person's vision. Could be 3 feet, could be 12 feet. –  AJ Henderson Jan 14 at 3:11

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