Birthday-problem calculator for hash spaces. Given a hash bit size and a number of generated items, compute the probability of at least one collision.
Supports scientific notation (e.g. 1e9, 2.5e12).
For n items in a hash space of size N = 2^bits, the approximate probability of at least one collision (birthday problem) is:
P ≈ 1 − e^(−n(n−1)/(2N))
The 50% threshold is reached at roughly n ≈ 1.1774 × √N.