How to use the birthday problem calculator
Find the chance two people share a birthday. Enter people, possible days in the fields above; the probability of a shared birthday is computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- n — People
- d — Possible days
Worked example
With people = 23, possible days = 365, the calculator gives probability of a shared birthday ≈ 50.00018 %.
Frequently asked questions
What is the formula for the birthday problem calculation?
Probability of a shared birthday (%) = 100 × (1-exp(-n × (n-1) / (2 × d))). Here n is people, d is possible days.
What inputs do I need for the birthday problem calculator?
You need people, possible days. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.