Technology & Computing
Hash Collision Probability & Birthday Attack Calculator
Estimate the probability of a hash collision occurring among a set of hashed items, based on the birthday paradox.
Your inputs
Change any value to update the result instantly.
Collision probability
0%
Hash space size (2^b)
1,15,79,20,89,23,73,16,20,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000
~50% collision threshold (items)
40,06,51,86,92,98,00,12,00,00,00,00,00,00,00,00,00,00,000
Items hashed
10,00,000
The birthday bound means collisions become likely after roughly the square root of the hash space size, not the full space.
Formula and working
P(collision) ≈ 1 − exp(−k^2 / (2 × 2^b)), computed as 1 − exp(x) with x kept in log space for numerical stability
- 1
Collect the inputs
Hash output length = 256; Number of hashed items (k) = 1,000,000
- 2
Apply the formula
P(collision) ≈ 1 − exp(−k^2 / (2 × 2^b)), computed as 1 − exp(x) with x kept in log space for numerical stability
- 3
Result
Collision probability = 0
Frequently asked questions
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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