Hash Collision Probability Calculator

A hash collision is when two different inputs produce the same hash output. The birthday paradox is the counterintuitive statistical result that collisions become likely far sooner than intuition suggests -- with a hash space of m possible values, you need only roughly the SQUARE ROOT of m random hashes (not m/2) before a collision becomes about 50% likely. That square-root figure is what Birthday Bound reports. This calculator's Hash Function selector picks a real, fixed digest length -- SHA-256 (256 bits), MD5 (128 bits), or SHA-1 (160 bits) -- and that selection determines the entire hash space size (2^length possible values), overriding the raw Hash Length field entirely, since all three available functions use a fixed, named digest size (a fourth option, Custom, lets you set Hash Length directly).

Collision Probability and Expected Collisions both depend on how many hashes you're comparing (Number of Hashes) relative to that space. For a modern 256-bit hash like SHA-256, the space is so astronomically large (2^256, which is still more atoms than exist in the Earth -- roughly 10^50 -- even though it's smaller than the ~10^80 atoms estimated in the observable universe) that even comparing millions of billions of hashes -- far beyond any realistic Number of Hashes this calculator accepts by default -- produces a collision probability and Time to Collision so close to zero that they round to 0 in the displayed output. This is the intended, correct behavior: it demonstrates why 256-bit hashes are considered collision-resistant for the foreseeable future, in sharp contrast to MD5 (128 bits), which is why MD5 is no longer recommended for security-sensitive hashing.