THE NUMBERS, EXPLAINED
How to use this calculator.
Birthday approximation for independent uniform hashes. This is accidental collision probability, not an adversarial security analysis.
Start with your inputs
Enter hash bits, items. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Hash bits | 64 |
| Items | 1000000 |
A worked example
With the example inputs above, approximate collision probability is 2.710503e-8. Change the inputs to explore your own scenario.
Putting the example numbers into the formula
Approximate collision probability
-expMinusOne(-(1000000) × ((1000000)-1) ÷ (2 × 2^(64))) = 2.710503e-8
| Result | Example answer |
|---|---|
| Approximate collision probability | 2.710503e-8 |
How this is calculated
Approximate collision probability
-expMinusOne(-b × (b-1) ÷ (2 × 2^a))
Symbols and units
- a
- Hash bits
- b
- Items
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
expMinusOne(x) calculates e^x−1 accurately even for small x.
Assumptions and limits
Birthday approximation for independent uniform hashes. This is accidental collision probability, not an adversarial security analysis.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Approximate collision probability. The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Birthday approximation for independent uniform hashes. This is accidental collision probability, not an adversarial security analysis.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
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