Birthday Probability Calculator
Find the chance that two people in a group share a birthday.
Last updated · View algorithm, constants and default inputs (JSON)
Probability of a shared birthday (%)
Dots show recalculated samples. Other inputs stay fixed.
About this calculator
This estimates the chance that at least two people share a birthday, assuming each day is equally likely; leap-day variation is not modeled.
Worked example
calculated with the default values below
People in the group 23 · Days in the year 365 Probability of a shared birthday 50.73 % · Probability nobody shares 49.27 % · Pairs in the group 253 · Odds against a match 1 to 1 · People needed for 50 per cent 23
Disclaimer
These calculators give general estimates for information and entertainment. Platform algorithms, metrics and definitions change without notice, and none of these results are official figures from the platforms named.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
P = 1 − Π_{i=0}^{n−1} (d−i)/d
- n
- Number of people
- d
- Possible birthdays in the year
- P
- Probability of at least one shared birthday
n is capped at 500 and d at 366; possible pairs = n(n−1)/2; peopleFor50 iterates multiplying by (d−k)/d until the no-match product first drops to ≤0.5.
Frequently asked questions
Why do just twenty three people give a fifty percent match chance?
This is the classic pair-match calculation: it estimates the chance that at least two people share a birthday, assuming each day is equally likely. It does not model leap-day differences.