I used to work in prepress. Still do some consulting in that space as well as handle print jobs from time to time. First love, blah blah…
In the print world, DPI and PPI can be used interchangeably. You’ll also see LPI thrown around from time to time (lines per inch) which is just another way of measuring print density in that world. LPI numbers are usually about half of their DPI counterparts (300 DPI is about 150 LPI).
Anyway, there’s a nifty little feature in Photoshop I use to figure out the effective print resolution of an image before it needs to be interpolated (i.e. synthetically generating more pixels, which degrades image quality). It’s all under the oft-used Image Size command.
I deal with 5K RED images often and one of our clients likes to pull stills for billboards and print ads. We generally capture in camera at 5120 x 2700 pixels. Open that image in Photoshop and do an Image Size command, this is what you get:
The trick to see how large that image can be printed at a given DPI/print resolution is to uncheck the Resample box and enter the DPI in the Resolution field. A common DPI for magazines is 300, so uncheck the box, enter 300 for Resolution and watch the dimensions change:
This is Photoshop saying that a 5120 x 2700 pixel image can be printed at 17 x 9 inches at 300 DPI with no interpolation required. Rotated vertically, that’s a full page in a magazine (US or A4 size) with room to spare. Again, without any interpolation or resampling.
So that’s a quick way to use Photoshop to do that math for you. Of course, you can check the Resample box and type in whatever dimensions you need and explore the various interpolation options available. But they will all degrade image quality in the sense they are making up pixels where none existed. No different than resizing in Flame and picking from the various options there (Lanczos, Bicubic, etc.).
I wouldn’t worry about CMYK conversion. Modern print systems and RIP software generally handle the RGB to CMYK conversion. They aren’t magic and will deal with out of gamut colors in different ways but I haven’t used Photoshop for a CMYK conversion in years because the tools work better in RGB. Just leave View > Gamut Warning enabled so you can see any issues and mitigate them so when the conversion to CMYK happens at the printer/RIP you don’t have big surprises. Think of it like doing a View Transform in the Colour Mgmt node in Flame, where the Display is a printer/press and the View Transform is whatever color calibration system/curve the print house has setup for their particular equipment. It’s sort of the job of the prepress nerds to ensure your RGB master is faithfully reproduced when the ink dries on the paper.
In the case of billboards, everyone here is right that billboards have incredibly low resolutions as expressed in DPI. They are meant to be seen far away, so having fine details serves no purpose. The video world equivalent would be the equation for viewing distance from a TV and how far away your eye can resolve the individual pixels that make up the image. Viewing a 4K TV from several hundred feet away would yield no benefit in resolution over the same size TV at HD resolution or even SD resolution, etc. Same principle.
A final note would be to echo what others have said: It’s usually sufficient to provide the highest resolution image you can without scaling up and let the billboard company worry about the rest. They have software solutions that deal with scaling tailored to their purposes so it’s far more efficient and less stressful to let them do their thing.
-Matt