Picture Resolution vs Printing Size

Pictures from a digital camera are taken at a resolution that depends on the capabilities of the camera sensor and on the camera settings.  The resolution of a picture is measured in pixels (horizontal) x pixels (vertical). The number of horizontal pixels multiplied by the number of vertical pixels gives the number of total pixels. The number of total pixels divided by 1,000,000 (the Mega prefix applied to pixels means 1,000 x 1,000 = 1,000,000) gives the number of Mega Pixels (MPx).

For example, my Canon EOS 7D camera has, when set to the M-RAW format (medium size RAW), an output resolution of 3,888 x 2,592.  This corresponds to 10,077,696 total pixels, which means 10.1 MPx.

It should be noted that often people (and photo processing software) are referring to a digital picture as having 72 DPI or 200 DPI. DPI stands for Dot Per Inch. The reality is that this information is per se meaningless until we want to actually print this digital picture. Then it assumes a meaning in relation to the size of the printing we want to obtain.

Back to the example above, here is the key question. If we want to print a 10.1 MPx picture, what is the maximum printing size we can aim for in order to have a “good” quality printing? Or in other words, above which printing size the printing quality will not be “acceptable” anymore stated that the digital picture file we want to print has 10.1 MPx?

In order to answer this question, it is necessary to agree on what means “good” or “acceptable” quality printing. Here is the answer. A “good” or “acceptable” quality printing is a printing which has a minimum of 200 DPI (for acceptable) or better at least 300 DPI (for good). Note that DPI quantity refers to the capabilities of the printer rather than to the resolution of the digital picture file we want to print. However if the printer is set to print, for example, at 1200 DPI but the resolution of our digital picture file allows only for 300 DPI, the printer will have to decide the value of 3 dots every 4. This operation is called interpolation and, if overdone, can bring to unsatisfactory results.

Back again. We have a 10.1 MPx (3,888 x 2,592 pixels) picture and, in order to obtain a “good” quality printing, we have to print it at at least 300 DPI. What is the maximum printing size we can obtain under this constraints and with no interpolation by the printer? Here is the math.

For the horizontal (long side) dimension:
3,888 pixels / 300 dots (pixels) per inch = 12.96 inches  (32.9 cm)

For the vertical (short side) dimension:
2,592 pixels / 300 dots (pixels) per inch = 8.64 inches (21.9 cm)

So the maximum printing size in this case would be 12.96 x 8.64 inches (or 32.9 x 21.9 cm). We could double each dimension accepting a 2 to 1 interpolation by the printer (“creating” 1 pixel every 2), but this would cause a decay in the overall quality.

The table below represents a generalization of what we just discussed. It crosses many possible resolutions with many possible printing sizes, indicating for each combination how many DPI can be obtained without interpolation by the printer. Combinations that  allows for 300 DPI or more are indicated with the green color. Combinations that allow between 200 DPI and 300 DPI are marked with yellow. The remaining combinations, which remain below the critical limit of 200 DPI are indicated in red.

The table can be used by choosing the resolution of the digital picture file we want to print and moving horizontally toward the right until the DPI value is green (or at the limit yellow). That is the maximum printing size which will allow a “good” (or “acceptable”) printing quality.

Picture Resolution vs Printing Size
Picture Resolution vs Printing Size

The following table refers specifically to the different output formats of the Canon EOS 7D (S-RAW, M-RAW and RAW).

Picture Resolution vs Printing Size (Canon EOS 7D)
Picture Resolution vs Printing Size (Canon EOS 7D)

(Click on each table to open a larger version).

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