Hash Collision Probability Calculator

Use the birthday paradox to estimate how likely it is that two different values produce the same hash. This calculator helps security engineers, database architects, and blockchain developers gauge collision risk before committing to a hashing strategy.

Use the total volume of hashes you expect (records, API responses, password attempts, etc.).
Enter the bit length of the hash function (MD5 = 128, SHA-1 = 160, SHA-256 = 256, etc.).

Assumes random, independent hash outputs; biased implementations may experience different results.

Examples

  • 100,000 hashes with a 32-bit hash (classic checksum) → 68.7539543116% chance of at least one collision.
  • 1,000,000 user IDs hashed with 64-bit output → 2.710505431e-06% collision probability (roughly 1 in 36,957,341,450).
  • 500,000 blockchain transactions hashed with 256-bit SHA-256 → 1.155557345e-68% probability, effectively zero in practice.

FAQ

Why does the birthday paradox model hash collisions so well?

Each hash is assumed to be uniformly random in a space of size 2^bits, just like birthdays are uniformly distributed across 365 days. Under those conditions the probability of any match follows the same combinatorial curve.

How many hashes can I generate before collisions become likely?

A common rule of thumb is to stay well below √(2^bits). For a 128-bit hash, that threshold is about 5.4×10^19 outputs—far beyond most applications.

Is this probability exact or an approximation?

The result is an approximation that treats every hash as an independent random draw. Real-world implementations with biased input, truncated digests, or poor randomness may experience higher collision rates.

What else should I monitor besides the collision percentage?

Consider the inverse odds (1/P) to understand how many hash events are expected before a collision, and combine that with business impact analysis to decide whether to enlarge the hash or add safeguards.

Additional Information

  • Formula used: P = 1 − exp(−n(n−1)/(2·2^b)), where n is the hash count and b is the bit length.
  • The collision curve accelerates once the number of hashes nears √(2^b); doubling bit length roughly squares the safe capacity.
  • Cryptographically secure functions (SHA-256, SHA-3) produce uniform output, but truncated or salted hashes can change the odds.
  • Plan mitigation strategies—deduplication, sharding, or larger digests—when the collision probability exceeds your tolerance.

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