For a photographer, the minimum viewing distance is limited only by the length of his nose. – Unknown
There are many rules of thumb for determining just how much resolution or pixels per inch (PPI) one needs to print for acceptable quality images. There are rules of thumb, and they are handy however, like most things in photography these things can be accurately quantified with relatively simple math but the numbers can be deceptive.
Some Rules of Thumb
Rules of thumb are usually a good place to start. However, like all rules of thumb in photography they should really be treated as suggestions not absolutes.
When it comes to resolution, the most common rule of thumb goes something like this: If the picture is 8” away, you need a source file with 480 pixels per inch (PPI), if the picture is 12” away you need 300 PPI, if the image is 24” away you need 180PPI.
What the rule doesn’t do is offer any idea as to how far away one would be from an image on average. For that, you need another rule of thumb.
One of the most common that I hear is that you should assume the image is viewed from a distance equal to the length of its diagonal. My personal experience with this is that doing that tends to be conservative for some, if not most, print sizes. For example, I tend to view 8x10s at about 18” not 13”.
What this ultimately comes down to is a question of the resolving power of the human eye. That has been measured to be 1 arc minute or 1/60th of a degree, for a person with 20/20 vision.
Using that measurement, we can work out the size of a spot a person with 20/20 vision would be able to see distantly at a given distance. Incidentally, this is not much different from the foundations for depth of field calculations.
A little trigonometry gets us started on the path to the spot size. Where Dspot is the spot size, and D is the distance to the print.
Using the spot size, we can compute the DPI as the reciprocal of the spot size. Putting it all togeather we end up with:
Plugging some numbers into the above formula, we get the following PPIs. For 8 inches, you need 430 PPI; for 12 inches, you need 287 PPI; for 18 inches, you need 191 PPI; and for 24 inches, you need 144 PPI. Not exactly what the rule of thumb listed but not horribly far off either.
As far as math goes, that’s it. The trick is figuring out how to interpret the numbers that come out of the equations.
In practice, the hardest thing to estimate is viewing distance, at least unless you have control over it somehow, like by having a desk or couch in front of the wall where the print is hanging. More than anything else, viewing distance has the largest impact on resolution especially when the distance is less than about 3-1/2 feet; dropping from more than 400 PPI to 100PPI in the 35 inches from 8 to 43 inches, but only dropping from 100 PPI to 45 PPI over the next 35 inches.
Yet it’s debatable if you’d ever want to print an image at 45 PPI or even 100 PPI. I know if I was selling a fine art print, I wouldn’t be comfortable with making a 24×36 from an 80PPI source even though the calculations suggest that is all that’s necessary at a viewing distance equal to the image’s diagonal.
Ultimately, it’s important to remember that these formulas provide the absolute lowest resolution you would ever want to print at, not necessarily my recommendations or even recommended resolutions. More resolution, if you have it available, is always going to give more “margin of error” since not everyone will abide by the estimates you might have started with.
I’ve posted a PPI calculator that will do the math for you as well as provide pixel and megapixel estimates for a given print size and viewing distance. In some ways it can be eye opening to see how little resolution is really visible for viewing distances longer than an arm’s length, or what’s actually needed if you went by the diagonal viewing distance rule of thumb.
Like most things in photography, there’s no easy answer. If you can control the viewing distance, there’s a lot of room for PPI to drop especially for large prints. However, doing so compromises their quality when viewed closer than that. How close or how far one has to consider that, though, is ultimately up to the photographer.