As I've said before, and to try to keep things simple, digital images are made up of pixels which have no 'linear' measurement to speak of.
A printer does not use pixels, it does use 'linear' measurement, it knows it has a piece of A4 paper to print on and it knows that A4 paper is a fixed width of 8.268".
For the printer to calculate how 'BIG' an image will be when printed it needs some correlation between the amount of pixels in the image and the amount of space in which it has to print.
That correlation is the DPI.
Your image can be printed at ANY size you require, and is set BY YOU using the DPI.
Changing the amount of pixels in an image is regarded as a no-no and should be avoided whenever possible.
If you need to change the OUTPUT size of an image, ie when its printed, then changing the DPI is prefered as opposed to changing the amount of pixels.
The amount of pixels in the image will determine the maximum size of the print given a certain DPI...
As I explained before your second image shows settings that will NOT work for an A4 piece of paper....the OUTPUT size is bigger than the paper.
PS should give you a warning about this if you tried to print it...something along the lines of 'The image is too large for the printer medium, some cropping will occur, continue?'
To overcome this you would increase the DPI so that the OUTPUT size becomes smaller and so fits the paper.
If you want your image to fit exactly onto A4 paper then adjust the DPI until the size is correct.
A4 is 8.268" wide.
Ignoring borders and gutters and suchlike this means with an image of 1221px wide the DPI would have to be 147.6. (1221 / 8.268)
Now, if this is not enough DPI for you, (as you would like 240+ preferably), then you are going to have to change something.
If you FIX the output size to A4 then the pixel dimensions have to change.
If you FIX the pixel dimensions then the OUTPUT size has to change.
By the sounds of it your only choice IS to upsample the image, despite this not being ideal it does seem to be the only choice you have.
To achieve 300dpi you will need an image of 2480px wide. (300 x 8.268)
This is 2.03 times the original size and just over 4 times the total number of pixels.
When you up-scale, use the 'image size' dialog in PS to change the width to 2480px.
Bicubic is fine but do try others, it can be image dependant as to how to the up-scaled image looks.
The DPI should change to 300 when you change the pixel width.
Keep 'Constrain Proportions' checked.
If you have any styles in your document you will want to scale those too so check that option as well.
With those new settings a value of 300dpi will give you an image exactly A4 in size so if you have any borders you will have to recalculate the pixels dimensions based on your requirements.
Regards.
MrTom.
