How do you find out? in LR, when you change the print size in Print module and print resolution tab is unchecked, resolution of print changes while you change the print size and it shown on the upper left side of the picture; what is the formula? how LR calculate that? when you check the resolution tab in LR and changing the print size, how should I find out what resolution should I chose for a given print size for best quality?
To determine the output resolution of a print, divide the native resolution of the image by the dimension chosen for a print. If the image has a native resolution of 21MP (like the 1DsMIII) which is 5616 x 3744 pixels and you wanted a 10 x 6.6 print, the resolution in terms of pixels per inch would be 561.6 PPI. You can also divide the native resolution by the desired output print resolution and determine the print size. That same 21MP capture would work out to 18.72 x 12.48 inches at 300 PPI or 15.6 x 10.4 inches at 360 or 31.2 x 20.8 at 180 PPI.
In terms of the resolution you "need" for a print, that depends on viewing distance because human vision resolution is dependent on the viewing distance. The close you hold a print to your eyes, the more resolution that your eyes can resolve. There's a chart on page 129 that tells you the eye's resolvable resolution. A couple of examples: viewing distance of 8 inches would require 428 PPI in PPI resolution. From 18 inches you would need 191 PPI.
From an article I did for Digital Photo Pro magazine called
The Right Resolution I wrote about what Bruce Fraser wrote about human vision acuity:
Resolution And The Eye
My good friend and colleague, the late Bruce Fraser, wrote about human visual acuity in his Real World Image Sharpening book (which I've taken over as coauthor for him). In the book, Bruce indicated that "the generally accepted definition of normal (20/20) visual acuity is the ability to resolve a spatial pattern whose features are separated by one minute of arc, or 1⁄60 of a degree." Unfortunately, that doesn't translate to printer-output resolution very easily. It involves trigonometry and calculations, which I hate. Fortunately, Bruce already did the math as shown in the table below.
Viewing Distance (in inches) Resolution the eye can resolve (DPI)
8" 428
10" 355
12" 286
18" 191
24" 143
As you can see, the closer the distance, the more resolution the eye can see when expressed as dots per inch (dpi). The normal viewing distance of a print is typically between 1.5 and 2 times the diagonal of a print. So a 3.5x5-inch print normally would be viewed from between 10 and 12 inches away, and the eye could resolve between 355 dpi and 286 dpi.
In terms of determining the usable range of output resolution, Bruce thought that depending on print size, you needed at least 180 PPI to a max of 480 PPI. However, I've found that depending on the printer, you can tell the difference up to about 720 PPI (assuming Epson, or 600 PPI for Canon or HP). This type of resolution is really only useful for small prints–which is handy because you'll have higher output resolution when making small sized prints.
The output resolution requirement is, of course, impacted by the size, printer, media and how well the original image was captured, and how the image and print was sharpened. Textured media is far more forgiving while glossy media requires as much resolution as you can give it.
In terms of the difference between image resolution and printer resolution, the output resolution of printers refers to droplets/inch. So, at 2880 the Epson printers put 2880 droplets of ink/inch. In terms of dots/inch, that's a different measurement–printers report their resolution to the print pipeline as dots/inch (DPI) which is a different measurement unit...Epson printer report 360 DPI which Canon HP report 300 DPI. There are driver modes that can change the reported resolution; Finest Detail makes Epson printers report 720 DPI while Canon & HP can be set to report 600 DPI.
Confused yet? Go back and reread the section in the book...