Nakamoto Coefficient
The Nakamoto coefficient is the smallest number of independent entities that together control enough of a blockchain's critical resource, such as hashrate or stake, to attack or halt it. Higher means more decentralized, at least in that one dimension.
Where the idea comes from
Balaji Srinivasan and Leland Lee proposed the measure in 2017 in an essay called Quantifying Decentralization, naming it after Bitcoin's pseudonymous creator. Their goal was to replace vague claims about decentralization with a number that could be compared across networks.
How it is calculated
First pick a subsystem, for example mining pools by share of hashrate, or validators by share of stake. Rank the entities from largest to smallest and add their shares until the total crosses the threshold that would give critical control. The number of entities needed is the coefficient for that subsystem.
The threshold depends on the attack. For proof-of-work, 51% of hashrate allows a majority attack such as rewriting recent blocks. Many proof-of-stake networks use Byzantine fault tolerant consensus, where more than one third of stake can stop the chain from finalizing, so their coefficient is often measured at 33%. The original paper suggested computing it for several subsystems, such as mining, client software, developers, exchanges and token ownership, and treating the smallest result as the network's overall coefficient.
A worked example
Say a proof-of-work chain has mining pools with these hashrate shares: 30%, 25%, 15%, 10%, 10% and 10%. The two largest pools together hold 55%, which is above 51%, so the mining coefficient is 2. On a proof-of-stake chain where the top validators hold 12%, 11% and 11% of stake, three of them reach 34% and could halt finality, so the coefficient at the one-third threshold is 3.
What the number does not tell you
The coefficient depends entirely on how entities are identified. A mining pool is not a single miner: thousands of independent hashers can switch pools if a pool misbehaves, so pool-based figures can overstate the concentration of control. The opposite also happens: several validators that look independent may be run by the same company or share one cloud provider, which makes the real figure lower than the published one.
It also measures only one subsystem at a time and only a snapshot. Governance, developer influence and software client diversity matter as much as hashrate or stake, and they are harder to count. Treat it as a useful starting question, not a final verdict.
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Frequently asked questions
What is a good Nakamoto coefficient?
There is no official cutoff. Higher is better because more independent parties must cooperate to attack, but comparisons only make sense when the same subsystem and threshold are used.
Why do proof-of-stake chains use a 33% threshold?
In Byzantine fault tolerant consensus, finality needs two thirds of stake to agree, so anyone controlling more than one third can block it.
Can the Nakamoto coefficient change over time?
Yes. It shifts whenever hashrate or stake moves between entities, so a figure from last year may no longer be accurate.
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