resolution – Is there a general formula for the size of the image compared to the size of the print?

I will sort of disagree with all the other answers that talk about empirical rules DPI or PPI, and suggest two different "rules" (based on PPD, taken from another of my answers)

Rule 1 – The Rule of the "Retina"

(aka the Pixel-Per-Degree (PPD) / Rule "better than your eye can see")

This comes quite directly from Apple's Retina display designs, the idea being that our eye can solve a certain number of pixels per degree. the resolution of the image / print must be taken into account with the desired viewing distance.

In short, Apple suggests a minimum of 53 PPDs, others up to 100 (especially if your vision is better than 20/20).

You can easily calculate one of the PPD, PPI and the distance of observation (re) on the basis of the other two:

PPD = d * IPP * 2 * tan (ft / 360) d * PPI * 0.01745
PPI = PPD / (d * 2 * tan (ft / 360)) ≈ PPD / (d * 0.01745)
d = PPD / (IPP * 2 * tan (ft / 360)) ≈ PPD / (PPI * 0.01745)

You may have a constrained IPP (if it is already printed), a constrained viewing distance (depending on the intended use or space limitations) and / or a PPD that you are trying to To reach (eg 75 to choose an arbitrary value between 53 and 100). Note that larger viewing distances than re the calculations are correct, it's simply going closer to allow viewers to "see the pixels".

If you ask this question long in advance, you can choose your PPP (and I suggest you choose at least 53, and anything beyond 100% is a useless effort) and, depending from your viewing distance, determine the required IPP. This tells you either the maximum print size (if the resolution of your camera is the limiting factor) and / or the required image resolution of your camera / photographer.

Examples

All that is held by hand can be seen as close as 15 cm (~ 6 "), although more likely about 25 cm (10"), so for 75 PPD, you would want 430 PPI (10 "), but even at 300 PPI, you get about 52 PPD at 25cm (10 "). If it's really a close-up visualization (or an enlarged visualization), you'll want to go well beyond 300 PPI (and you'll have to determine the effects of any enlargement to obtain an appropriate PPD).

Anything framed or wall mounted is more likely to be viewed from 50 cm (20 ") to 2 m (80"). So, for 75 PPDs, you would need about 215 to 55 PPIs, respectively.

A display panel can be designed to be viewed at a distance of 10 m (33)). A print format of 75 PPP (11 PPP) would be enough for printing (go look at a poster board or a very large poster close up, the pixels of the photo are often clearly visible and several mm wide).

Rule 2 – The rule of & # 39; 45 & # 39;

(aka the rule of "comfortable viewing distance" / rule "yes, your camera is good enough")

It is a simplification of the first rule, which applies to any image you will only see in its entirety. That is, you do not come closer to see the details (as in a group photo, a large panorama, a magazine product photo, etc.). This can be anything from a framed photo to a huge billboard, to prints hanging on walls and galleries. For most people, I think that would apply to most of their images.

The basic idea is that you will see the picture as a whole, so the larger it is, the longer the viewing distance is. I will define the "comfortable viewing distance" as "the distance at which the image fits into a 45º field of view", which happens to be about the same as the field of view of a 45mm lens on a 35mm / full frame camera (and is vaguely similar to the FoV of your eye in some ways).

That's an arbitrary number, and you can adjust accordingly, although if you have a specific context or space in mind, you probably use the first rule anyway (after all, it's not the same thing). It is only a simplified version for a specific use case).

Since the required IPP depends linearly on the viewing distance and the viewing distance depends linearly on the size of the image and the size of the image depends on the resolution and the PPI. The IPP ends up canceling and you can simply calculate the required resolution according to the desired PPD and FoV angle (I've chosen 45).

For an angle of 45º, it ends up being simply:

dimensions in pixels = desired PPD x 45 (replace 45 by the desired viewing angle)

Again, the useful PPD ranges are between 53 and 100, and useful viewing angles can range from 20 to 60 (even if you do not really see the whole picture, go back to rule 1) .

So, for our arbitrary requirement of 75 PPD and our 45º viewing angle, we would like an image of about 3400 pixels wide (2250×3375 ~ 8 megapixels), still.

The resolution of the required image is static if the viewing angle is fixed.

For the lowest PPD of Apple (53), this could be as low as ~ 1600×2400 (~ 4MP) and for the higher requirements of 100 PPD you would need ~ 3000×4500 (~ 14MP). Even if it is not a very high resolution with current cameras (my old 450D only has 12 MPa).

And this is why some people claim that a specific (and often quite weak) resolution is perfectly suited to all situations (objectives in which the image is viewed as a whole, regardless of the distance chosen for the size of the print ).

I have an impression of the size of a poster made from a 6 MP photo (from my old 450D, for which I was shooting in JPEG at half a resolution), but you will not notice never that it is printed at "only" ~ 75 DPI because it is mounted on the wall and there is no reason to get close to it and use it in a personal way (other than the pixel peep) . Most of the time, seen between 1 and 2 meters, corresponds to about 53 to 107 PPD.

In defense of the minimum rules DPI / PPI

Although I do not like the strict rules DPI / PPI, the flip side is still valid is that particularly high print resolutions (for example, in magazines / brochures on paper glossy) add a sense of quality / precision that goes beyond anything. see the pixels at the expected viewing distance. The viewer may not look more closely at individual photos to see their details, but perhaps take a closer look at the magazine / brochure itself (not necessarily intentionally) and become aware of the quality of print ( or his absence).

Also, if your viewers are voyeurs at the pixel.