Calculator (or forumla) to calculate DPI for a given size and viewing distance?

[sirhawkeye64]

Looking for a pretty straightforward answer here if possible as I know some people may choose a higher than required DPI for some things/reasons, but I'm just looking for the basic formula that i can use. I seem to remember when I looked at this years ago, that CoC comes into play somewhere as well, and for reference, on my camera's its 0.03 which I think it is on many FF cameras.

Anyway, does anyone know of or have this formula/calculation they can share? I'm starting to do prints, and usually I have just resorted to doing 300 dpi regardless, but am starting to think taht for longer viewing distances, I may not need such as high DPI (and that something like 240 might work for say 3-4 ft away versus 1-2 ft).

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[NAwlins Contrarian]

Looking for a pretty straightforward answer here if possible as I know some people may choose a higher than required DPI for some things/reasons, but I'm just looking for the basic formula that i can use. I seem to remember when I looked at this years ago, that CoC comes into play somewhere as well, and for reference, on my camera's its 0.03 which I think it is on many FF cameras.

Anyway, does anyone know of or have this formula/calculation they can share? I'm starting to do prints, and usually I have just resorted to doing 300 dpi regardless, but am starting to think taht for longer viewing distances, I may not need such as high DPI (and that something like 240 might work for say 3-4 ft away versus 1-2 ft).

I can and will give you a math formula, but I think this is the wrong approach. Do not resize or sample your image before sending it to be printed. Do not send a printer anything other than its native resolution (300 ppi on most printers, but 360 ppi on some Epsons, except in 'finest detail' mode). Instead, let good software resample from however many pixels you have (based on cropping to the proportions i.e. aspect ratio of the print size you want) to however many pixels the printer will natively use, and don't worry about it. And by good software I mean (1) if having a good professional service make the print, then whatever software they use to process your file for their printer; and/or (2) if printing yourself, then good printing software like Qimage or Lightroom Classic. The large majority of the time, for the large majority of images, the results will look fine.

Now that math: there is no fixed answer, and much depends on your own standards of what's 'good enough' and the nature and contrast of the detail in the image. But one crude and generalized way of looking at it is that the limit of 'normal' but '20/20-type' human vision is sometimes regarded as about 0.5 minute-of-angle (MOA). A minute is 1/60 of a degree, i.e., the limit of angular visual discernment with fairly high-contrast detail is about 1/120th of a degree. So the trigonometry is:

TANGENT(0.5/60) = visible detail size / viewing distance

so

visible detail size = viewing distance * TANGENT(0.5/60)

so

visible detail size = viewing distance * 0.000145

so e.g. at 3 ft = 36 in, visible detail = 0.00522 in = 1/192 in so 192 ppi

and at 1 ft = 12 in, visible detail = 0.00174 = 1/575 in so 575 ppi.

To convert from the decimal of an inch to ppi, just just the reciprocal function (1/x on most calculators).

Again, that's about the limit of 20/20 human vision, albeit subject to many footnotes and qualifiers.