How big can I print my image?

"Zoom into this image so that the width of each vertical line is 1 mm or the whole image is 3.2 inches wide."

Is it possible to pick one system? Also, "3.2 inches" is difficult to measure. Rulers that measure in less than an inch use fractions, not decimals. It usually goes by 1/8ths, then 1/4 and 1/2, but some rulers have 1/16ths. 3/16" is .187 inches which is pretty close I guess.

Half-in-jest, I think we should put some pressure on the International Bureau of Weights and Measures to standardize dots per meter (DPM), and then have the EU follow through with a new law or two to accelerate adoption.

Unfortunately printers print in dots though, not pixels. There are printers with variable dot sizes, supposedly a thing with professional print, I wouldn't know - but nominally a dot is gonna be one of the four ink colors (cyan, magenta, yellow, black) and then it's either present or not present. I'm sure someone who didn't sleep only just one hour overnight can calculate you how many dots you need to cover the same gamut as a typical 24 bit SDR RGB pixel will.

Good luck printing anything at 870dpi.

This whole article is a bit confused. Image quality isn’t about the ability to discern detail. Many people cannot see the detail in their 4k TVs or a photo, it’s about not seeing visible pixelation.

Those aren’t the same thing. Visible pixelation is connected to contrast and color depth. That’s why a perfectly smooth gradient appears as bands of color in poorly encoded images and video. There’s no detail in gradients at all. The pixelation is due to a lack of color information.

On top of that printers use different numbers of colors (from 3 to 11 or more) and different ways of sizing and layering dots (if you aren’t using continuous tone printers which are very rare nowadays).

Then you have to add in the ability to up res images plausibly using modern algorithms. Whereas before we were always stretching the data we had, now by adding false detail using ML we can scale a significant amount without a visible reduction in quality. That can be very effective at removing pixelation while preserving the original image content.

So in reality there aren’t hard and fast rules. It’s totally image and output dependent.

tl;dr:

    Viewing distance PPI
    1 meter          170 pixels/inch

which is to say that a 12mp image is going to max out at 18x24"