Bloom Filter Calculator: Size, Hashes & Error Rate

A Bloom filter answers 'have I seen this?' in a fixed number of bits, at the price of occasional false positives, never false negatives. Its behaviour is set by three numbers — the bits m, the hash functions k and the items inserted n — and this calculator solves for whichever you are missing: the smallest filter that holds n items at a target false-positive rate, the rate a filter of a given size will have, or how many items fit before the rate is exceeded. The rate is the standard (1 − e^(−kn/m))^k, evaluated so that targets as small as 1e-300 keep full precision. Most calculators size the filter with the continuous formula −n·ln p / ln²2 and then round k to a whole number, which quietly lands a little above the target — 4,000 items at 1e-7 gives 134,191 bits with 23 hashes and an actual rate of 1.0006e-7. This one searches for the smallest m whose best whole k really meets the target (134,196 bits here) and tells you when the usual answer falls short. Leave k blank for the best integer value, or fix it to see what your implementation's hash count costs. A load table shows how the rate climbs as the filter fills past its design size — at twice the design load, a 1 % filter is closer to 16 %. The formula assumes independent, uniformly distributed hash functions; two hashes combined as h1 + i·h2 (Kirsch–Mitzenmacher) are close enough in practice, but a weak hash or correlated keys will do worse than any figure here. The memory shown is the bit array alone, without the per-structure overhead of any particular library; counting and scalable Bloom filters need more.