What is the Nakamoto Coefficient and How Do You Calculate It?

What is the Nakamoto coefficient?

The Nakamoto coefficient is a tool to assess the degree of decentralization. It was proposed in 2017 by Balaji Srinivasan, former CTO of cryptocurrency exchange Coinbase and creator of the Network State concept, in co-authorship with Leland Li.

In a paper dedicated to the tool, Quantifying Decentralization, they compared over-centralization to inequality in the economy based on the synergy of the two indicators:

• The Lorenz curve, a graph of a mathematical function that shows the distribution of income or wealth. The greater the deviation from the line, the greater the inequality. In the blockchain industry, it can reflect the distribution of computing power or tokens among network participants;
• Gini coefficient is a statistical indicator of the stratification of society by income distribution. The range from 0 to 1 indicates the degree of inequality.

The authors of the article reflect on the lack of quantification of decentralization. Their basic idea is as follows:

• List the key subsystems of a distributed system;
• determine the number of individual elements to compromise in order to gain control over each of them;
• use the minimum value of the resulting numbers as an indicator of effective decentralization.

The Nakamoto coefficient reflects the minimum number of organizations (mining pools, validators, or other stakeholders) needed to collectively disrupt or take control of a network. By calculating the ratio for any network, you can understand how difficult it would be for attackers to attack it.

What data are used to calculate the coefficient?

Srinivasan and Lee noted the impact of subsystems on the accuracy of the calculation. To apply the concept to the realm of public blockchains, it is necessary to separate the system from its elements.

Using the bitcoin network as an example, there are six subsystems of decentralization:

1. Mining. In PoWnetworks, miners confirm transactions. The more widely distributed the mining power, the greater the decentralization. In PoS systems, validators are similarly evaluated.
2. Software customers. Customer diversity reduces the risk of a single point of failure..
3. Developers. Distributed participation of engineers in blockchain updates protects against a small group taking control of the project.
4. Exchanges. A large concentration of tokens on several trading platforms increases the risk of manipulation.
5. Nodes. Nodes distributed across countries and operators make the network more resilient.
6. Token ownership. The distribution of large BTC balances is evaluated.

To calculate the final Nakamoto coefficient, the minimum value of all subsystems under study is taken. Centralization of one element reduces the overall decentralization level of the network.

What is the Nakamoto coefficient of Bitcoin and Ethereum?

The calculation process involves several steps:

1. Identification of key actors. Identification of the main players in the network - mining pools, validators, node operators, token holders..
2. Assessing the level of control. Analyzing power distribution, such as hash rate in PoW or rate share in PoS..
3. Summarizing elements. Sorting the participants in descending order and counting their number to reach 51%, the critical value for attacking the network.

For an example, consider bitcoin with the following structure of mining pools as of May 1, 2025:

• Foundry USA - 30.6% hashrate;
• AntPool - 17.1%;
• ViaBTC - 15.4%;
• F2Pool - 9.8%;
• MARA Pool - 5.6%;

• Others - 21.5%.

To count:

• Foundry USA = 30.6%;
• AntPool (30.6% + 17.1% = 47.7%);
• ViaBTC (47.7% + 15.4% = 63.1%).

When the ViaBTC pool was added, the total value crossed the 51% threshold with an indicator of 63.1% - the summation is complete. According to the calculation results, the three pools control more than half of the network, which means the Nakamoto coefficient for bitcoin is 3.

Given its decentralized nature with a large number of working bitcoin nodes, distributing computing power among pools can create risks for the network. The task of the Nakamoto factor is to point out the weak elements. 

The second most capitalized cryptocurrency Ethereum, despite an impressive number of nodes, also does not boast a high degree of decentralization when calculating the share of stakers by PoS consensus mechanism.

When performing a similar calculation, the Nakamoto coefficient for Ethereum is 5. The 51.2% threshold is crossed by summing the shares of ETH staking in Lido, Coinbase, Binance, Ether.fi and Kiln.

How else is the Nakamoto coefficient being used?

PoS networks like Sui and Aptos operate on an architecture of mixed DAG-BFT consensus mechanisms. Such systems require the agreement of only 2/3 of the validators to validate a block. In other words, control over more than 66.6% of tokens allows to actually control block creation. 

According to analytical resource Nakaflow, Nakamoto Ratio scores among PoS networks are patchy. As of May 1, 2025, one of the lowest values - only 4 - is observed for Polygon. Blockchains Solana, Cardano, Avalanche, THORChain and Avail have average values between 20 and 35. The record holder by a wide margin is the Polkadot parachain network with Nakamoto's 173 odds.

Some blockchain creators are using the Nakamoto coefficient in an attempt to perfect their technology.

For example, the team of startup Internet Computer posted a study of decentralizing the network using a modified version of the tool in their technical documentation.

The developers noticed that for their project, using a minimum factor value is not always the correct way to assess risks. For example, it is inappropriate to distribute network participants in the sample by continent: the risk of collusion among node providers is not necessarily related to their geographical proximity. At the conclusion of the analysis, the experts came to the use of a weighted average of the coefficient for all subsystems.

The Internet Computer subsystems included the following elements:

• dapps. Applications used by the community are controlled by DAO NNS or individual organizations;

• protocol management. Supervised by the NNS and is responsible for the code running in the nodes of the network;

• infrastructure layer. This is the physical layer of Internet Computer, reflecting the participation of network nodes. It is also managed by the NNS.

The developers noticed that it is more logical to show the dynamics of changes. For example, an increase in the Nakamoto factor from 1 to 2 in a subsystem is critical because it means that there is no longer a single point of failure in the network. This change is more critical than an increase from 10 to 11. 

Given that a weighted average would reflect both changes equally, the Internet Computer team suggested using a weighted average of the logarithms of the ratio values to reflect significant changes.

What are the drawbacks of the tool?

The Nakamoto Ratio is a simple tool to estimate the minimum number of participants needed to control a network. It helps understand the distribution of power and assess the security, reliability, and resilience of blockchain platforms.

The metric informs developers, investors, and users, driving improvements in governance models, consensus mechanisms, and scalability solutions to increase decentralization.

But the Nakamoto coefficient has a number of drawbacks:

• Staticity. Shows the state of the network at a particular point in time. Since participation is constantly changing, the data quickly becomes outdated.
• takes into account only onchain data. It is important to remember that multiple validators can belong to the same owner;
• focus on subsystems. Evaluates only a fraction of pruvers or miners, but ignores factors of client software diversity, geographic distribution, or concentration of token ownership;
• does not take into account the high cost of investment to start a node, which indirectly affects decentralization;

• the need to adapt calculations to different consensus mechanisms;
• external influences. Regulatory measures, technological changes and market dynamics, can affect network decentralization, something the Nakamoto factor does not account for.