One estimate that I saw says that on average there are about 20-40 million hairs on a cat, but, of course, this would vary due to breed, how big the cat is, etc. Since a certain amount of shedding is normal, that many hairs leaves room for an enormous amount to be shed in a year.
Cats shed some every day and go through one to two large sheds and hair growth cycles per year. The shed cycles vary with each cat and cats ingest so much hair when they groom themselves that you almost never see clumps of it.
Cats shed enough that a furnace repairman once told me that he advised cat owners to check their furnace filters more often because of the large amount of cat hair that gets sucked into them!
As for how much fur a cat sheds over the course of a year there is some anecdotal estimates that full regrowth can be achieved over 8 to 12 weeks, but that does not give any answer with regards to the actual mass.
Of course, the answer depends on the cat's size, type of hair and environment and the amount will vary depending on temperature (lighter fur in summer, denser in winter). Also, the growth rate vary with the temperature. Therefore, there isn't a simple answer valid for all cats.
Based on unsubstantiated estimates of the number of hairs a cat has, the average thickness and the average growth rate of the hair one estimate claimed a cat could shed total of up to 5.5 pounds per year. Naturally, that was a wildly unscientific figures and it could be way off.
In the end, there are way too many factors involved to give an even halfway accurate answer, but if you have ever owned a cat you know the answer is, "a lot!"
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