Uniform Random Value Collision Calculator
Calculate the chance that independent uniform draws repeat a value within an entered namespace.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Multiply the successive no-repeat factors using logarithms, then evaluate one minus that probability with expm1 to retain small collision tails. Compare with expected equal-value pairs.
P(no repeat)=∏(1−i/N), i=1..n−1; expected equal-value pairs=n(n−1)/(2N)
Worked example
With 23 independent uniform draws from 365 values, the repeated-value probability is about 50.7297%. With two draws it is exactly 1/365 under the model.
Assumptions and input details
Independent uniform draws from the same fixed namespace, with replacement. This is a mathematical collision model, not a test or certification of a generator. Expected equal-value pairs differ from expected duplicate draws. Namespace size is shown as an exact integer; probabilities use floating point and may round to 0 or 1.
References: Stanford CS109: birthday probability
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Calculate exactly k, at most k and at least k successes in independent trials. Explore the binomial distribution, expected value and standard deviation.
Count ordered or unordered selections, with or without repetition. Read the exact integer result, compare all four cases and list examples for small problems.
Expand and normalize a hexadecimal IPv6 address and calculate exact numerical prefix boundaries and child-prefix counts.
Reserved advertising space.