Can a mathematical function that has been in use for over 130 years predict the long-term price of Bitcoin? The Bitcoin Power Law is exactly such a theory: it holds that Bitcoin's price will grow with its "age," exhibiting a predictable long-term trajectory. The logic is simple—Bitcoin will keep rising, but as it ages, the rate of increase will gradually slow.
How does the power law apply to Bitcoin?
A power law describes a mathematical relationship in which a change in one quantity is proportional to a fixed power of another quantity. Such relationships are common in nature, physics, and economics, and appeared as early as the 17th-century research of astronomer Johannes Kepler. Physicist Giovanni Santostasi discovered that Bitcoin has been enacting this mathematical pattern since its early days.
Imagine a tree: it grows extremely fast when young, and as it ages it still grows taller, but the percentage growth gradually declines. The Bitcoin power law holds that Bitcoin behaves similarly. According to Santostasi's model, each time Bitcoin's age doubles, its long-term trend price rises by roughly 50 times.
For example, suppose an asset follows this law: at 10 years the trend price is $1,000, at 20 years it is $50,000, and at 40 years it is $2.5 million. As can be seen, the same 50-fold increase took 10 years the first time and 20 years the second time. This is also why the model predicts that Bitcoin will continue to rise, but with annual returns gradually narrowing.
How accurate is the model?
Bitcoin has experienced violent crashes and surges throughout its history, yet its long-term price trajectory has consistently stayed remarkably close to the same mathematical curve. People favor this model for three main reasons: first, it is mathematically simple enough to estimate the long-term price path using only Bitcoin's age; second, it has a possible economic explanation—as adoption increases, network value rises, and Santostasi believes this network growth explains the price curve; third, its predictions are striking enough—the current model gives a price of about $1 million for 2033.
The theory gained more attention in 2026: Santostasi and Stephen Perrenod published a peer-reviewed study supporting the relationship between network adoption and Bitcoin's price.
High historical fit, questionable future predictions
In terms of describing Bitcoin's long-term price trend, the power law is currently accurate; but its ability to predict future prices is far less certain. The 2026 study examined 5,696 daily Bitcoin prices between July 2010 and February 2026, and the model explained about 96% of the variation in Bitcoin's historical log price. But this does not mean its price predictions are 96% accurate.
There is also some evidence supporting its predictive value: independent researchers from several universities in Portugal found that, over 12- to 24-month forecast horizons, a simple power-law model outperformed the other approaches they tested. However, they likewise question whether this mathematical relationship is truly stable and whether it is fundamental.
The model also has an obvious weakness. Historically, Bitcoin's bull-market peak prices have been far above the power-law trend line: the 2013 peak was about 11 times the trend price, while by 2025 this multiple was only about 1.2 times. This could indicate that Bitcoin is becoming a more mature asset, or it could mean the model is beginning to overestimate future growth.
How realistic is the $1 million target?
The power law is more of a useful long-term benchmark than a reliable price target. Its greatest value is identifying that, across more than 15 years of extremely volatile trading history, Bitcoin has followed a relatively stable growth path.
But a fundamental question remains unanswered: does Bitcoin follow this curve because a lasting economic relationship exists, or does the curve merely describe what happened during Bitcoin's extraordinary early adoption phase? When extrapolating 10 or 20 years into the future, this distinction is crucial. The $1 million prediction for 2033 is mathematically self-consistent with the model, but whether Bitcoin can actually reach it depends on whether this growth pattern continues.
