Calculators
Handshake Calculator
Count unique handshakes and single or double round-robin matches using exact browser arithmetic.
Count unique pairs when every participant meets every other participant once. Enter a non-negative whole number of up to 100 digits. Calculations stay in your browser.
How to count unique pairs
With n participants, every participant can meet n − 1 others. Multiplying n by n − 1 counts each unordered pair twice, so the number of unique handshakes is n(n − 1)/2, also written C(n, 2). For 10 participants there are 45 pairs and 9 meetings per participant. Zero or one participant gives zero pairs. This assumes everyone meets everyone else exactly once, with no self-pairings. The same count gives the total matches in a single round-robin tournament; a double round robin has n(n − 1) matches. This counts matches, not rounds, simultaneous playing slots or a schedule. All participants are distinct and there are no excluded pairings. Enter a non-negative integer of up to 100 decimal digits. Surrounding whitespace and leading zeros are accepted; decimals, signs, separators and scientific notation are rejected. BigInt arithmetic keeps all result digits exact. Results and inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Why divide by two?
Counting n times n − 1 includes both A meeting B and B meeting A. They are the same unordered pair, so divide by two.
How many matches do 10 teams play?
A single round robin has 45 matches, with 9 per team. A double round robin has 90 matches.
Does this generate a tournament schedule?
No. It counts total pairings. It does not assign rounds, venues, byes or playing times.
Can the participant count be zero?
Yes. Zero or one participant produces zero pairs. Counts must be non-negative whole numbers with at most 100 digits.