# Digital image size in pixels and photo print size

This article is about the relation between an image size in pixels and a photographic print size. First, it recommends the photographic print size for given digital image dimensions in pixels. Second, it finds the resulting pixels per inch value for a printed digital image with known linear and pixel dimensions.

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#### Anton

Created: 2011-11-25 21:49:32, Last updated: 2020-12-16 13:03:34

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The first calculator recommends the photographic print size for given digital image dimensions in pixels.

Let's define the problem:
We have a digital image with the known size in pixels, for example 3264 x 2448, and we also have a known set of standard photo print sizes used by photographic printing services. The photo print size name defines the linear dimensions of a photo print – for example, 4''x6'' or 4R photo print size means that the photo print has 102x152 millimeters dimensions.

We want to choose the maximum photo print size that allows us to print the digital image without quality loss.

I've created the handbook Standard photographic print sizes for defining standard photo print sizes, which can be edited to provide missed sizes.

The only special knowledge we needed to solve the problem was about quality, which was easily found on the web. Photographic quality (at an arm's length viewing distance) requires that the print resolution should be no less than 300 DPI (dots per inch), which can also be written as 300 PPI (pixels per inch). A still-acceptable quality requires that the print resolution should be no less than 150 DPI. Armed with this knowledge, everything else is simple math.

Look at the picture below

Each photo print size is converted to pixels, assuming that 1 inch holds 300 (150) pixels. The obtained size in pixels (taking into account the aspect ratio, more on this below) is compared to the digital image size. If the print size in pixels is greater than the digital image size (see picture, print size on the right), then it will not fit, since we would have to enlarge the image and the resulting resolution would be worse than 300 DPI. If the print size in pixels is less than the digital image size (see picture, print size on the left), then it would fit, since we have to shrink the image and would obtain a resolution better than 300 DPI.

The calculator chooses the print size with the maximum linear dimension that will fit. (A smaller size isn't a problem since we can print with resolution up to 1200 DPI.)

#### Photo print size

Recommended size for 300 dpi photo print or better

300 dpi photo print size in pixels

Recommended size for 150 dpi photo print or better

150 dpi photo print size in pixels

The second calculator in this article finds the resulting pixels per inch value for a printed image and how many pixels were cropped during scaling.

Let's define the problem.

We have a photo print with known dimensions in centimeters, printed from a digital image with known dimensions in pixels. Usually, the aspect ratio of a printed image is not the same as the aspect ratio of digital image. The image is scaled during printing, but its aspect ratio remains constant. This leads to unwanted effects.

Look at the picture below

We have two ways to scale:
first – scale with cropping out part of image
second – scale without cropping, but with empty spaces on the photo print.
Since the second looks ugly, I used the first.

Thus, we have to find the resulting image resolution in DPI, and how many pixels were cropped due to the difference in aspect ratio. The first one is easy – the dimension in pixels (width or height) that is not cropped is divided by the corresponding photo print dimension in inches. The second one is the difference between used pixels on the cropped dimension and the original digital image pixels.

#### Pixels per inch

Width of printed image (cm)
Height of printed image (cm)
Width of digital image (pixels)
Height of digital image (pixels)
Printed image aspect ratio

Digital image aspect ratio

Used width (pixels)

Used heigth (pixels)

Printed image resolution (DPI or PPI)

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PLANETCALC, Digital image size in pixels and photo print size