k = items

N =

- probability (exact):
- probability (approximate):
- relative error of approximation:

If you put 'k' items in 'N' buckets, what's the probability that at least 2 items will end up in the same bucket? In other words, what's the probability of a hash collision? See here for an explanation.

If you specify the units of N to be bits, the number of buckets will 2^{N}.

Due to numerical precision issues, the exact and/or approximate calculations may report a probability of 0 when N is very large (N=2^{128}, for example), when in fact the probability is just very very small. Similarly, they may report a probability of 1 when the probability is very very close to 1. The approximate method is more robust. If you're using large N, like N=2^{128}, then keep adding 0s onto k and you should eventually get a non-zero answer.