Calculator inputs
Example data table
| Hash bits | Items | Hash space | Approx. collision probability | Expected colliding pairs |
|---|---|---|---|---|
| 16 | 150 | 65,536 | 15.68% | 0.1705 |
| 24 | 5,000 | 16,777,216 | 52.52% | 0.7449 |
| 32 | 50,000 | 4,294,967,296 | 25.25% | 0.2910 |
| 64 | 10,000,000 | 18,446,744,073,709,551,616 | 0.000271% | 0.0000027 |
Formula used
Hash space: m = 2^b, where b is the number of hash bits.
Exact no-collision probability: P(no collision) = ∏(1 - i / m) for i = 0 to n - 1.
Birthday approximation: P(collision) ≈ 1 - e^(-n(n-1)/(2m)).
Expected colliding pairs: E[pairs] = n(n-1)/(2m).
Expected occupied slots: E[occupied] = m(1 - (1 - 1/m)^n).
Expected duplicates: E[duplicates] = n - E[occupied].
50% threshold: n₅₀ ≈ √(2m ln 2).
Target threshold: nₚ ≈ √(2m ln(1/(1-p))), where p is the desired collision probability.
How to use this calculator
- Enter the hash length in bits for the system you want to study.
- Type the number of current records and the projected future record count.
- Set the collision probability target that matters for your design decision.
- Add an estimated hashing speed to translate thresholds into approximate time.
- Choose reduced toy bits and paste sample labels for the demonstration table.
- Click Calculate collision metrics to show the result block above the form.
- Use the CSV button for spreadsheets and the PDF button for a printable report.
FAQs
1. What does this calculator actually find?
It estimates how likely collisions become for a chosen bit length and record count. It also shows expected duplicate behavior and a toy sample demonstration.
2. Why is it called a finder if it uses probability?
Real collision discovery for secure hashes is not practical here. This tool finds risk thresholds, expected collision pressure, and toy collisions in reduced sample space.
3. When is the exact method used?
The exact product is used for manageable item counts and moderate bit sizes. Larger cases switch to the birthday approximation for stable performance.
4. What is the birthday approximation?
It is the standard shortcut for estimating collision probability in large hash spaces. The approximation is highly useful when exact multiplication becomes expensive.
5. What does expected colliding pairs mean?
It measures the average number of record pairs that land in the same slot. It is useful even when total collision probability seems small.
6. Why does the toy sample table use CRC32?
CRC32 is quick and widely available for demonstration. The table intentionally truncates it, making educational bucket collisions easy to observe.
7. Can I use this for database keys or deduplication design?
Yes. It helps compare bit sizes, dataset growth, and acceptable risk before choosing identifiers, sharding rules, or checksum-based storage workflows.
8. What should I do if the collision probability is high?
Increase the hash length, reduce records sharing one namespace, or redesign partitioning. Lower load per hash space quickly reduces collision pressure.