The power law, known to science for over 130 years, is capable of describing the long-term price trajectory of the leading cryptocurrency. According to this model, Bitcoin will reach the $1 million mark by 2033.
The model is based on the power law — a fundamental regularity that describes an asset's trajectory through a basic mathematical function. The essence of the relationship is simple: one quantity changes proportionally to another raised to a certain power. This principle is widely found in nature, physics, and economics, and its earliest examples date back to the astronomer Johannes Kepler in the 17th century.
Bitcoin becomes more expensive as it matures, but the growth dynamics fade over time. Physicist Giovanni Santostasi noticed the same pattern in Bitcoin even at the early stages of its existence. The model resembles the growth of a tree: while it is young, it grows quickly, but as it ages, the rate declines.
How the power law works for Bitcoin
According to Santostasi's model, each time Bitcoin's age doubles, its long-term trend price increases by approximately 50 times. Here is how this looks using the example of a conditional asset following this law:
- 10 years — $1,000
- 20 years — $50,000
- 40 years — $2,500,000
Note: the same 50-fold increase takes first 10 years, then 20 years. The model assumes that Bitcoin will continue to grow, but annual returns will be increasingly lower.
How accurate the power law model is for Bitcoin
Bitcoin has survived massive drawdowns and rallies, but in the long term its price follows one mathematical curve with surprising precision. The model has three reasons that make it convincing for many.
- It is mathematically simple. The model uses Bitcoin's age to estimate its long-term price trend.
- There is an economic explanation. The more people come into Bitcoin, the higher the value of the network. The network effect explains the shape of the price chart.
- The model makes bold predictions. According to current calculations, Bitcoin's price in 2033 will reach approximately $1 million.
The theory gained particular significance in 2026, when Santostasi and Stephen Perrenod published a peer-reviewed study confirming the link between the growth of the network effect and Bitcoin's price.
Assessments of the accuracy of the Power Law model for Bitcoin
The rule describes past events excellently, but future performance remains in question. In a 2026 scientific paper, the authors studied 5,696 daily values from July 2010 to February 2026. As a result, the mathematical function explained about 96% of the variations in the logarithmic price over the specified period. However, this does not at all guarantee similar accuracy for real forecasts.
Scientists from Portuguese universities tested the algorithm's performance in practice. According to their data, the simple Power Law model predicts values 12–24 months ahead better than alternative methods. Nevertheless, the researchers questioned the stability of the fundamental relationship.
The system has a tangible flaw. Previous bull cycle peaks deviated significantly from the trend line. For example, in 2013 the maximum exceeded calculations by almost 11 times. By 2025, the anomaly had shrunk to 1.2 times. Such dynamics indicate either the market's maturation or that the formula itself is beginning to overestimate future results.
How realistic it is to see Bitcoin at $1 million
The Power Law system serves as a guide for the vector of movement, not a guarantee of a specific figure. The main achievement of the authors lies in finding a pattern across 15 years of colossal volatility. Experts are concerned with the main question: is the asset moving along the chart because of fundamental laws, or does the curve merely reflect the initial adoption boom? The difference will become critical over a 10–20 year horizon. Nevertheless, the $1 million mark by 2033 looks logical from a mathematical standpoint. The main thing is for the coin to maintain the given pace.
Cryptalist analysis: The power-law model demonstrates high explanatory power on historical data, but its predictive value remains a subject of scientific debate. Institutional investors should view $1 million by 2033 as a long-term trend guide rather than a guaranteed target, since the shrinking peak anomaly points to a possible transformation of the very nature of the relationship as the market matures.