Configure hash space and workload
Formula used
Let N be the number of possible hash outputs (the “hash space”), and k be the number of distinct items hashed.
- P(no collision) = ∏i=0k−1 (1 − i/N)
- P(≥1 collision) = 1 − P(no collision)
- Birthday approximation: P(≥1 collision) ≈ 1 − exp(−k(k−1)/(2N))
- Expected colliding pairs: E ≈ k(k−1)/(2N)
The calculator assumes outputs are uniformly random over N. If an attacker can influence inputs, collision resistance and design choices matter more than raw probability.
How to use this calculator
- Pick a hash family, then adjust output bits or truncation if needed.
- Enter your expected item count k; or set a rate and duration to derive it.
- Choose Auto for fast results; use Exact only for small k.
- Set a target probability to estimate how many items reach that risk.
- Use CSV/PDF buttons to share results with your team.
Example data table
| Scenario | Bits | Items (k) | Approx collision probability | Notes |
|---|---|---|---|---|
| Short identifiers | 32 | 100,000 | ~0.688 | High risk when space is small. |
| Truncated output | 64 | 1e9 | ~0.0268 | Still non-trivial at large scale. |
| Legacy 128-bit output | 128 | 1e18 | ~0.00147 | Risk depends on workload growth. |
| Modern 256-bit output | 256 | 1e12 | ~4e−54 | Accidental collisions are negligible. |
| Large dataset tagging | 64 | 5e9 | ~0.50 | Near the classic birthday threshold. |
FAQs
1) What does “collision probability” mean here?
It is the chance that at least two of your k hashed items share the same output value, assuming the output behaves like a uniform random draw from N possibilities.
2) Why does truncating outputs increase collision risk?
Truncation reduces the number of possible outputs from 2^b to 2^t. Since collisions scale roughly with k²/N, shrinking N makes collisions appear much sooner.
3) What is the difference between expected collisions and collision probability?
Expected colliding pairs estimates how many matching pairs you’ll have on average. Collision probability is the chance of at least one collision. For small risks, they are nearly the same.
4) When should I use Exact mode?
Use it only for relatively small, integer k values. It directly computes the “no collision” product with log-summing, which is accurate but slower for large workloads.
5) Does this reflect real-world cryptographic security?
It estimates accidental collisions under a uniform-output assumption. Security against chosen-input attacks depends on the algorithm’s collision resistance and whether attackers can shape inputs.
6) How many items cause a 50% collision chance?
Roughly 1.177 × √N. The calculator shows this as “k for 50% chance,” which is the classic birthday threshold for random draws.
7) What if I need “virtually zero” collision risk?
Increase output bits, avoid truncation, and keep unique prefixes or namespaces separate. If risks are still high, store full outputs or add secondary checks before treating a match as identical.
8) Can I model time-based growth?
Yes. Enter a hash rate and duration to derive k, or use the target probability field to estimate how long it takes to reach a chosen risk level at your rate.