The dimension in pixels (Image Size) is the important detail for using any image.
Around 300 pixels per inch is an optimum and proper printing goal for photographs. 200 dpi can sometimes be acceptable quality, but printers cannot do 400 dpi (not for color photos).
There are two situations when printing images.
Either way, it is good if your plan properly prepares the image for printing. First cropping the image so that the image SHAPE actually matches the selected paper SHAPE is also an important concern. Different paper sizes are different shapes.
Long dimension fitted
Short dimension fitted
Aspect Ratio is the "shape" of the image - the simple ratio of the images long side to its short side, maybe long and thin, or short and wide. And every paper size seems to be a different shape too. To print an image, we can always enlarge the Size, but the image Shape needs to match the paper Shape (which is a crop). If this Aspect Ratio subject is new, see Image Resize.
The calculator below specifies just one paper dimension, either the short or long one. That dimension is fitted to the paper, and the other dimension will float (will vary, to be whatever the image shape actually is). Ideally, you will have already cropped the image shape to match the selected paper shape properly. Otherwise, you may get a surprise about what image area has been cropped off.
The idea is to first crop the image to be the same shape as the selected paper. See Image Resize about how to handle this necessary resize and/or crop.
The calculator below asks if your print should be fitted to the Long or the Short image dimension. If you have already properly cropped your image to match paper shape, then it doesn't matter which you choose, both long and short results will match the paper shape.
The straight-forward way to scale for printing is to simply compute "pixels per inch" for the inches scanned, and then recompute those pixels over the inches printed (called scaling, as mentioned in the scanning Results). The scanner will have its Input and Output dimensions to show this. Also we have photo editor tools to make this resize be easy. See Image Resize and Scaling.
However a shortcut for the same scaling concept is this:
The ratio of (scanning resolution / printing resolution) is the enlargement factor.
For example (in general - speaking of any size original):
Scan at 600 dpi, print at 300 dpi, for 600/300 = 2X size (to print double size or 200% size)
Scan at 300 dpi, print at 300 dpi, for 300/300 = 1X size (to print original size or 100% size)
Scan at 150 dpi, print at 300 dpi, for 150/300 = 1/2X size (to print half size or 50% size)
Or scan small film at 2700 dpi, print at 300 dpi, for 2700/300 = 9X size. If from full frame 35 mm film (roughly 0.92 x 1.41 inches), then 9X is about 8x12 inches (near A4 size). Film is typically small, requiring more scan resolution for more pixels for more print enlargement. The reason to scan at high resolution is to create enough pixels to print larger at about 300 pixels per inch.
This is called "scaling", and this enlargement concept is true for scanning anything, photo prints, documents, film, etc.
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