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Birthday Collision Probability Calculator — result sheet
Calculate the probability that at least two people share a birthday under a uniform-day model.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(shared birthday) = 1 − ∏(i=0 to n−1)((D−i)/D).
The complement is easier to calculate: first find the probability that every birthday is different, then subtract it from one.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of people — minimum 1; maximum 366
- Possible birthday days — minimum 1; maximum 10000
Worked example
| Input | Value |
|---|---|
| Number of people | 23 |
| Possible birthday days | 365 |
Shared-birthday probability ≈ 50.73%.
Assumptions and limits
- Every day is equally likely and birthdays are independent.
- The number of people cannot exceed the number of possible days for the no-collision product.
- Leap-day patterns, seasonality, and demographic effects are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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