What this chart shows
Metcalfe's Law, originally proposed for telecom networks, states that a network's value is proportional to the square of the number of connected users (n²). Several researchers have tested variants of this idea against Bitcoin, using daily active addresses as a proxy for users. This page runs that regression itself, live, rather than quoting a specific paper's coefficient.
A fitted exponent b near 2 would support a pure Metcalfe relationship; a lower exponent would suggest network value scales with usage more slowly than the square law predicts. The legend states whatever this page's fit actually finds today.
How to read it
The gauge shows actual price as a multiple of what the fitted Metcalfe relationship predicts for today's active address count. Readings near 1× mean price is tracking the fitted relationship; readings far from 1× mean price has detached from what address activity alone would suggest.
Limitations — why active addresses is a leaky proxy for users
One person can control many addresses (a new address per transaction is common practice), and one address can be shared by many people (exchange hot wallets). Active address count is a noisy, imperfect stand-in for the number of actual distinct people using the network.
Like Power Law and Stock-to-Flow, this regresses two series that both trend upward over Bitcoin's history — which tends to produce a deceptively high R² regardless of whether one genuinely drives the other.
There is no settled academic consensus on whether Metcalfe's Law even holds for cryptocurrency networks, or what the "correct" exponent should be. Different studies using different address-counting methodologies have found different values.