Birthday Paradox Calculator

Your details

Forward: enter the number of people and get the probability. Reverse: enter a target probability and get the minimum group size needed.
The number of people in the group. Must be at least 2.
people
Use 365 for a standard year, 365.25 to average in leap years (one extra day every four years), or 366 for a leap year.
Probability of a shared birthdayMore likely than not
50.7297%

Chance that at least two people in the group share the same birthday

Number of birthday pairs253
Probability of no shared birthday0.4927%
Effective group size used23people
50.7297%
Very unlikely<10%Unlikely10%-50%More likely than not50%-75%Highly likely75%-99%Near certain99%+

50.73% chance of a shared birthday in a group of 23.

  • With 23 people there are 253 possible birthday pairs. Each pair adds a small chance of a match, and those chances compound quickly.
  • The 50% threshold is crossed at 23 people, and a 99% probability is reached at 57 people. Both numbers feel surprisingly small.
  • This is the classic birthday paradox: intuition expects a much larger group because we compare our own birthday against everyone else, but there are far more pair comparisons happening than that.

Next stepThe probability is already above 50%. Removing just a few people drops it noticeably. Try the reverse mode to find the exact threshold for any target.

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