Metcalfe's Law
A network's value scales with the square of its users.
Robert Metcalfe, 1980. The quantitative form of network effects. If a network has n users, the number of possible connections is roughly n × (n-1) / 2, which scales as n². Double the users and you roughly quadruple the value.
The math has been disputed (some networks scale linearly, others super-quadratically), but the directional point is right: large networks are dramatically more valuable than small ones, in a way that compounds.
For operators, Metcalfe's Law explains why winner-takes-most dynamics emerge in networked products. The second-largest network isn't half as valuable as the largest; it's much less. The math drives consolidation.
Examples in the wild
Marketplaces with 100 sellers and 1000 buyers aren't 10x more useful than ones with 10 sellers and 100 buyers; they're more like 100x more useful. The non-linear value drives the winner-take-most outcome.
Companies positioned to dominate networked markets often justify high prices because of Metcalfe dynamics. The capture value is concentrated.
Personal networks compound this way too. A network of 1000 useful contacts isn't 10x more valuable than 100; it's many times more, because of the cross-connections.
Metcalfe's Law is one of the mental models we apply through real cases inside the Pareto MBA — a part-time program for professionals who want to think clearly about business.