|Hopefully you've arrived here after reading most of the information on this website. So, you should know that the DPI setting within a digital photo is meaningless in the context of the digital photo itself. You'll understand the fact that a digital photo of say 3,000 x 2,000 pixels with the DPI set to 72 is identical to that same digital photo with the DPI set to 300 (except for those two DPI numbers in the photo). If the only change to those photos was to change the DPI number, then the photos are identical in both size and quality. But, to clarify, let's do some simple arithmetic.
DPI/PPI Printed Size
When a print shop or magazine asks you for a "300 dpi" photo, that request in itself is absolutely meaningless (there is no such thing as a 300 dpi, or any dpi digital photo). What they are asking for is a photo that will print at 300 pixels per inch (and this has nothing directly to do with the DPI setting inside the photo). To know if you have a suitable digital photo for that purpose, you need to know their intended output. If they tell you they need a digital photo that can print at 300 ppi to 7 inches by 5 inches then you can do the math.
We can turn this upside down and ask - if I have a 3,000 pixel wide digital photo and print it at 7 inches - what is the ppi? It's just 3,000 divided by 7 inches = 428.6 ppi. If you print that same photo to 11 inches, it will be printing at 272.7 ppi. It's just simple arithmetic.
To clarify that the DPI setting inside the photo is meaningless in terms of the digital photo itself, if it was set to 300 and you printed the 3,000 pixel wide photo at 7 inches, it will still be printing at 428.6 ppi. It's only meaningful if your software uses it to set the output dimensions, in which case your 3,000 pixel photo will print at 10 inches (at 300 ppi). But if you set the internal DPI of that photo to say 150 (without re-sizing the photo), and printed it at 10 inches, it will still be printing at 300 ppi.
DPI/PPI Digital Size
The size of a digital photo is its pixel dimensions. But how big will it print to paper? Say you have a 3,000 x 2,000 sized digital photo. Let's do the math:
DPI to PPI when scanning
Both Photo A and Photo B will be printing at 584 ppi (3504 divided by 6 inches and 2336 divided by 4 inches). The DPI setting in the photo doesn't make a difference, they are both exactly the same photo.
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