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Statistical · fitted

Metcalfe's Law

Metcalfe's Law says a network's value scales with the square of its number of users. This page fits Bitcoin's market cap against its daily active address count and shows you the exponent it actually finds, live, rather than asserting a number.

Data: CapMrktCurUSD, AdrActCnt, SplyCur, PriceUSD · Coin Metrics community API · computed live in your browser, nothing uploaded

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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.

log₁₀(Market Cap) = a + b · log₁₀(Active Addresses)

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.

Further reading

Metcalfe's Law and Bitcoin: Valuing Network Effects by Active Addresses

FAQ

What is Metcalfe's Law?
Originally describing telecom and social networks, it states that a network's value scales with the square of its number of connected users — because the number of possible connections between users grows quadratically as users are added.
Does Bitcoin actually follow Metcalfe's Law?
It's debated. This page runs the regression live and shows you the actual fitted exponent rather than asserting an answer — check the legend to see what today's data implies, and judge for yourself how close it is to the theoretical value of 2.
Why use active addresses instead of a better measure of users?
Because address count is the closest proxy publicly available on-chain. Real user counts (accounting for shared exchange addresses and one person's multiple wallets) aren't observable from blockchain data alone — this is a genuine, acknowledged limitation of every version of this analysis, not just this page's.