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There is no way to tell, even if someone wanted to count how many are actually mentioned in the movies or books because, as shown in The Half-Blood Prince's copy of Advanced Potion-Making, jinxes, hexes, charms, spells, curses, ect. can be invented by anyone, even if they are never "ministry approved", tested professionally or well-known.

It's like asking how many cooking recipe's there are in the world.

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