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See the odds that two people in a group share a birthday, with the head count needed to reach 50, 95, and 99 percent. Group size 2 to 100, any day pool.

📘 How to Use

  1. Set the group size with the slider
  2. Enter the day pool (usually 365)
  3. Read the shared-birthday chance and the head count for 50/95/99 percent

Birthday Paradox Calculator

Shared-birthday chance
— %

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50% threshold
— people
95% threshold
— people
99% threshold
— people
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※ Formula: 1 - product(1 - i/D) for i in 1..N-1 (D = days, N = people). Assumes uniform birthdays

※ Seasonal trends, leap years, and twins make real-world rates run slightly higher

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Birthday Paradox Calculator | Shared-Birthday Odds and Head Count

Enter a group size and see the chance that at least two people share a birthday, plus the number of people needed to reach 50, 95, and 99 percent.

💡 About this tool

"In a room of 23 people, there is a better-than-even chance two of them share a birthday." That counterintuitive fact is the birthday paradox. Most people guess you need roughly 180 people, since there are 365 days. But the number of possible pairs grows fast, so the odds cross 50 percent at just 23.

Drag the slider from 2 to 100 people and the shared-birthday chance updates as you go. Check a classroom, a sports roster, a team standup, or a party guest list. The day pool defaults to 365 but is fully editable, so you can model any "collision" problem: shared locker codes, raffle numbers, or hash buckets.

🧐 Frequently Asked Questions

Q. Why does it cross 50 percent at 23 people? A. With 23 people you can form 253 distinct pairs. Multiply the no-match probability of every pair together and the chance that nobody shares drops to about 49.3 percent, which flips to a 50.7 percent chance that someone does.

Q. At what point is a match almost certain? A. The odds pass 99 percent at 57 people. The "99% threshold" card shows that head count for any day pool you enter.

Q. Is this the same as someone matching MY birthday? A. No. The paradox asks whether ANY two people match. The odds of someone matching one specific person are far lower and grow much more slowly.

Q. Can I change the day pool away from 365? A. Yes. Set any value from 2 to 3,650 to explore how a larger or smaller pool changes the collision odds.

Q. Does it handle leap years and Feb 29? A. The math assumes birthdays are spread evenly across the pool. Set the pool to 366 for a leap-year approximation, though real-world rates run slightly higher because of seasonal trends and twins.

📚 Why the Birthday Attack Matters

Developers meet this paradox again as the "birthday attack" in cryptography. An N-bit hash is expected to produce a collision after roughly 2^(N/2) inputs, not 2^N, which is exactly the square-root behavior you see here. Swap the day pool for a power of two and the calculator becomes a quick gut-check for hash collision risk. It is a favorite Stack Overflow and security-interview example precisely because the answer feels wrong until you do the multiplication.