I keep reading that the p arm is shorter than the q arm. But I cannot find an explanation of how much shorter nor an explanation for the difference.
It varies from chromosome to chromosome and from species to species. In some cases, both arms are roughly the same length. In some cases, one arm is so short that it is almost inexistant. For chromosomes with equal length arms, of course the terms p and q do not apply.
p and q are used to describe the relative size of the arms of a chromosome. According to this wikipedia article p stands for petite (french for small) and q is just the next letter in the alphabet.
So p is just defined as the smallest arm in any chromosome. How much smaller is not relevant for this definition. The names are just jargon which make it easy to refer to an arm.