Birthday Paradox Calculator
Calculate birthday paradox using your data.
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What this tool does
Calculate birthday paradox using your data. Birthdays are assumed equally likely across the chosen number of days and independent between people (no twins, no seasonal effects). With 23 people there are 253 pairs — that is why a match passes 50%.
How to use the Birthday Paradox Calculator
- Enter or select people in the group.
- Enter or select possible birthdays.
- Read the calculated result; change any measurement to compare alternatives.
Formula
P(at least one shared birthday) = 1 − Π (days − i)/days for i = 0…people−1; 1 when people > days
- people
- People in the group
- days
- Possible birthdays
Birthdays are assumed equally likely across the chosen number of days and independent between people (no twins, no seasonal effects). With 23 people there are 253 pairs — that is why a match passes 50%.
Worked example
For birthday paradox calculator, the following measurements illustrate the exact method: People in the group: 23; Possible birthdays: 365.
Inputs
- People in the group23
- Possible birthdays365
Result
- P(at least one shared birthday) (%)50.73
- P(all birthdays distinct) (%)49.27
- Pairs of people253
Results explained
- P(at least one shared birthday) (%)
- P(at least one shared birthday) (%) from the formula above. Birthdays are assumed equally likely across the chosen number of days and independent between people (no twins, no seasonal effects). With 23 people there are 253 pairs — that is why a match passes 50%.
- P(all birthdays distinct) (%)
- P(all birthdays distinct) (%) from the formula above. Birthdays are assumed equally likely across the chosen number of days and independent between people (no twins, no seasonal effects). With 23 people there are 253 pairs — that is why a match passes 50%.
- Pairs of people
- Pairs of people from the formula above. Birthdays are assumed equally likely across the chosen number of days and independent between people (no twins, no seasonal effects). With 23 people there are 253 pairs — that is why a match passes 50%.
Frequently asked questions
P(at least one shared birthday) = 1 − Π (days − i)/days for i = 0…people−1; 1 when people > days
Birthdays are assumed equally likely across the chosen number of days and independent between people (no twins, no seasonal effects). With 23 people there are 253 pairs — that is why a match passes 50%.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.