Handshake Calculator

About this calculator

The classic handshake problem asks how many total handshakes occur if everyone in a room of n people shakes hands with everyone else exactly once. The answer is n(n−1) ÷ 2, the same formula as nCr with r = 2, choosing 2 people out of n to form each unique pair, since every handshake corresponds to exactly one unordered pair of people.

This same choose-2 structure underlies counting the number of games in a round-robin tournament where every team plays every other team once, the number of edges in a complete graph with n vertices in graph theory, and the number of possible one-to-one connections in a network, which is why it is a staple introductory combinatorics problem used to build intuition before moving to general nCr calculations.

Enter the number of people, or teams, or nodes, and this calculator returns the total number of unique handshakes, matches, or connections.