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Birthday Probability Calculator

The birthday paradox: chance that at least two people in a group share a birthday — 23 people already gives over 50%.

Enter values

Results update as you type.

Result

P(at least one shared birthday)

50.7297%

P(all different)
49.2703%

About the Birthday Probability Calculator

The birthday paradox: chance that at least two people in a group share a birthday — 23 people already gives over 50%.

Also known as: birthday paradox, shared birthday probability, birthday problem.

How to use this calculator

  1. Enter people in the group.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Review the breakdown shown under the main result.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

P = 1 − (365/365)(364/365)…((365 − n + 1)/365)

Worked example

Using the values pre-filled in the calculator above:

  • People in the group = 23

the calculator returns:

  • P(at least one shared birthday): 50.7297%
  • P(all different): 49.2703%