How many hash functions does my bloom filter need?

Question

Wikipedia says:

An empty Bloom filter is a bit array of m bits, all set to 0. There must also be k different hash functions defined, each of which map

Answer 1

Given:

• n: how many items you expect to have in your filter (e.g. 216,553)
• p: your acceptable false positive rate {0..1} (e.g. 0.01 → 1%)

we want to calculate:

• m: the number of bits needed in the bloom filter
• k: the number of hash functions we should apply

The formulas:

m = -n*ln(p) / (ln(2)^2) the number of bits
k = m/n * ln(2) the number of hash functions

In our case:

• m = -216553*ln(0.01) / (ln(2)^2) = 997263 / 0.48045 = 2,075,686 bits (253 kB)
• k = m/n * ln(2) = 2075686/216553 * 0.693147 = 6.46 hash functions (7 hash functions)

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