Some pixel math equations:

Three things characterize any digital picture. It has print size (both height and width), it has a given number of pixels along an edge of the print, and it has resolution which is a measure of how many pixels fit into an inch of the picture at its current size.

If you are given the number of pixels along one edge and the resolution, calculate print size of that edge by dividing pixels by resolution.
i.e.     print size (inches) = pixels/resolution

If you are given resolution and size, calculate pixels by multiplying size by resolution.
i.e.    number of pixels = print size (inches) x resolution

If you are given number of pixels and print size, calculate resolution by dividing pixels by print size.
i.e.    resolution = number of pixels/print size (inches)

One consequence of this pixel math is that if you halve the resolution of an image while retaining its rectangular dimensions (print size), you halve the number of pixels in the image. You are throwing information away, for better or worse.

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NOTES: You must be working in one measurement system for these equations to work. Don't mix millimeters and inches in any one equation. Instead, make all measurements uniform by using one of the following formulas:
    1) to convert mm to inches, divide mm by 25.4
    2) to convert inches to mm, multiply inches by 25.4


Changing Resolution in Photoshop

To change resolution of an image, you use the Image, Image Size dialog box. It lets you change print size, resolution, and the number of pixels in an image. It can be tricky to use though if you don't understand certain principles.

Pay special attention to the choices in the Image, Image Size dialog box when you change resolution or size of your image. In particular the Resample Image checkbox affects profoundly the way that Photoshop handles resizing or resolution changes.

If Resample Image is checked, pixels are either thrown away or added to the picture. Remember that adding pixels does not add sharpness - they are generated through interpolation.

If Resample Image is unchecked, Photoshop keeps the same number of pixels in the picture even though the picture is resized. The same number of pixels means that the file size remains constant, and all you are doing is redistributing the pixels in space. The resolution changes because the same number of pixels must fit in a different sized space. Pixels packed into a smaller space mean a higher resolution, while the same pixels in a larger picture mean lower resolution. Remember that resolution is the number of pixels that fit in an inch.

Practice using this dialog box and learn what the different controls do. Notice when things are grayed out and understand why do so when certain choices are made.