Could a mathematical function that has stayed relevant for over 130 years predict Bitcoin’s long-term price?
The Bitcoin Power Law is a mathematical theory that says Bitcoin’s price follows a predictable long-term growth pattern based on how old Bitcoin is.
The idea is surprisingly simple. Bitcoin keeps growing, but its growth slows as it gets older.
How Does the Power Law Work in Bitcoin’s Context?
The Power Law is a mathematical relationship that scientists have studied for centuries, with early examples appearing in the work of astronomer Johannes Kepler in the 1600s.
It describes how one quantity changes in proportion to another raised to a fixed power, often appearing in nature, physics, and economics.
Physicist Giovanni Santostasi saw this mathematical pattern play out in Bitcoin from the early days.
Imagine a tree. When a tree is young, it grows very quickly. As it gets older, it continues growing, but its percentage growth slows.
The Bitcoin Power Law suggests Bitcoin behaves similarly.
According to Giovanni Santostasi’s model, every time Bitcoin’s age doubles, its long-term trend price increases roughly 50 times.
For example, imagine the trend price of a hypothetical asset following this law:
| Age | Trend price |
| 10 years | $1,000 |
| 20 years | $50,000 |
| 40 years | $2,500,000 |
Notice the same 50-fold increase takes 10 years initially, then 20 years.
That’s why the model predicts Bitcoin will continue rising while delivering progressively smaller annual returns.
How Accurate is the Bitcoin Power Law?
Bitcoin has experienced enormous crashes and rallies, yet its long-term price history has stayed remarkably close to one mathematical curve.
There are three reasons people find it compelling.
- It’s mathematically simple. It uses Bitcoin’s age to estimate its long-term price trajectory.
- It has a possible economic explanation. As more people adopt Bitcoin, the network becomes more valuable. Santostasi argues this network growth explains the price curve.
- It makes striking predictions. The current model puts Bitcoin at approximately $1 million in 2033.
The theory became particularly significant in 2026 when Santostasi and Stephen Perrenod published a peer-reviewed study supporting the relationship between network adoption and Bitcoin’s price.
Is the Power Law Historically Accurate?
So far, yes, at describing Bitcoin’s long-term price trend. Its ability to predict future prices is less certain.
The 2026 study examined 5,696 daily Bitcoin prices from July 2010 to February 2026. The model explained approximately 96% of the variation in Bitcoin’s historical logarithmic price.
This does not mean its price forecasts were 96% accurate.
There is also some evidence of predictive usefulness. Independent researchers from Portuguese universities found that the simple Power Law performed better than the alternatives they tested for forecasts 12–24 months ahead.
However, they questioned whether the mathematical relationship is truly stable and fundamental.
The model also has a notable weakness.
Historically, Bitcoin’s biggest bull-market peaks were much higher than its Power Law trend.
In 2013, the peak was almost 11 times the trend. By 2025, it was only around 1.2 times the trend.
That could reflect Bitcoin becoming a more mature asset. It could also suggest the model is starting to overestimate future growth.
How Realistic is Bitcoin Price to $1 Million?
The Power Law is more of a useful long-term benchmark rather than a reliable price target.
Its greatest achievement is identifying a relatively stable growth pattern across more than 15 years of exceptionally volatile Bitcoin trading.
But there’s a fundamental unanswered question: Does Bitcoin follow this curve because of an enduring economic relationship, or does the curve simply describe what happened during Bitcoin’s extraordinary early adoption?
That distinction matters enormously when projecting another 10 or 20 years into the future.
The $1 million prediction for 2033 is mathematically consistent with the model. Whether Bitcoin actually reaches it depends on the growth pattern continuing.
