Beginner DPI question.

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Ben
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Is it really necessary to resize at 300dpi for an A4 print? I've been looking at different printers to get some of my photos done and they seem to ask for high DPI even for smaller prints. Or have I got this the wrong way around, would a smaller DPI be more suitable for larger prints with bigger viewing distances?
 
DPI = Dots Per Inch on the printed medium (so think about that in relation to your last point) and is specifically related to printing and basically it is number of MP/size of the image and neither of those are that important unless you know the viewing distance.

That little box on Lightroom where you can specify DPI doesn't actually do anything to the image, it just changes the number in the little box to keep printers happy.
 
Typically (assuming 20/20 vision) the eye can't resolve better than...

800dpi at 4" (the closest a perfect human eye can focus - and usually uncomfortable)
300dpi for magazine viewing distance (12")
115dpi for monitor viewing distance (30")
50dpi for TV viewing distance (6 feet)
7dpi for cinema screen viewing distance (40 feet)

So in short...
would a smaller DPI be more suitable for larger prints with bigger viewing distances?

Yes.

Whatever typical distance you're going to be examining your photo from is where you should go. An image best viewed at 40 feet and thus printed at 7dpi will look pretty bad up close. Just get your nose against any billboard poster to see. If (for example) you're entering A3+ prints for competitions or exhibitions where you might have people up close to check quality - you may want to go higher.
In real world terms, I can get away with 80-100 dpi on the walls at home no matter what physical size they are. I've got a 13"x19" print of a monitor screenshot that looks absolutely fine. iPhone prints to A3+ easily.
 
Is it really necessary to resize at 300dpi for an A4 print? I've been looking at different printers to get some of my photos done and they seem to ask for high DPI even for smaller prints. Or have I got this the wrong way around, would a smaller DPI be more suitable for larger prints with bigger viewing distances?

Most tend to stick with common rule of a thumb guidelines which is: 300dpi for printing (photo prints, magazines, posters, etc., anything on paper) and 72dpi for display on screen. Never mind if a printer suggest a much higher dpi for smaller prints, the machine do not order you which dpi setting to use, you are in change of the machine. Stick with 300dpi, and if you're worried it don't look right, feel free to adjust, try 150dpi or 100dpi until you feel it looks right.
 
Being a pedant... it is ppi not dpi, the latter refers to the printed image i.e. dots per inch laid down by the printer on the paper.

Displayed on screen then the ppi makes no difference it is the pixel dimensions that count, i.e. an 800px x 600px image at 10ppi will display the same size as an 800px x 600px image at 100ppi on screen.

The relationship between ppi and pixel dimensions will and does make a difference when going to print and the final (native) size of the print, i.e using the same example as above the 100ppi image will print smaller than the 10ppi image even though the pixel dimensions are the same.

So by reducing the ppi you can print larger whilst retaining the pixel dimensions, the larger the print the greater the viewing distance will be so the lower ppi will have no real effect.

Most commercial printers will suggest a ppi setting for your files, their software will do a good job of resizing the file for various sizes, 300ppi is always a good starting point.

As others have stated experiment a little.
 
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