What a Long-Standing Scaling Rule Suggests for Bitcoin by 2033

Could a mathematical function with more than 130 years of staying power forecast Bitcoin’s long-term price?

According to the Bitcoin Power Law, a mathematical theory, Bitcoin’s price tracks a long-term growth pattern that can be predicted from the age of Bitcoin.

The concept is remarkably straightforward: Bitcoin continues to expand, yet the pace of that expansion eases as it ages.

What Role Does the Power Law Play for Bitcoin?

Scientists have examined the Power Law, a mathematical relationship, for centuries; the astronomer Johannes Kepler provided early examples in the 1600s.

It explains how one quantity varies in proportion to another raised to a fixed power, and it frequently turns up in nature, physics and economics.

Giovanni Santostasi, a physicist, observed this mathematical pattern taking shape in Bitcoin from its early years.

Consider a tree. A young tree expands very fast. With age it keeps expanding, yet its percentage growth falls.

The Bitcoin Power Law holds that Bitcoin follows a comparable path.

In Giovanni Santostasi’s model, a doubling of Bitcoin’s age corresponds to an increase of roughly 50 times in its long-term trend price.

To illustrate, consider what the trend price would be for a hypothetical asset subject to this law:

At 10 years, the trend price is $1,000; at 20 years, $50,000; at 40 years, $2,500,000.

Observe that the same 50-fold gain requires 10 years at first and 20 years later.

This is why the model forecasts further gains for Bitcoin, accompanied by annual returns that shrink over time.

What Is the Track Record of the Bitcoin Power Law?

Bitcoin has endured huge rallies and crashes, but over the long term its price history has tracked a single mathematical curve with striking closeness.

Three factors help explain its appeal.

• The math is simple. Bitcoin’s age is used to estimate where its price might trend over the long term.
• There is a plausible economic rationale. The network gains value as adoption widens, and Santostasi contends that this network growth accounts for the price curve.
• Its predictions are striking. Under the current model, Bitcoin is placed at about $1 million in 2033.

The theory gained particular prominence in 2026, when Santostasi and Stephen Perrenod published a peer-reviewed study that backed the link between network adoption and Bitcoin’s price.

Has the Power Law Held Up Historically?

In describing Bitcoin’s long-term price trend, it has succeeded so far. Whether it can forecast future prices is less clear.

The 2026 study looked at 5,696 daily Bitcoin prices between July 2010 and February 2026. About 96% of the variation in Bitcoin’s historical logarithmic price was explained by the model.

That does not make its price forecasts 96% accurate.

Some evidence also points to predictive usefulness. Researchers at Portuguese universities, working independently, found that the simple Power Law outperformed the alternatives they tested for forecasts 12–24 months ahead.

They did, however, question whether the mathematical relationship is genuinely stable and fundamental.

The model carries a notable weakness as well.

In the past, the largest bull-market peaks in Bitcoin stood well above the Power Law trend.

The 2013 peak reached nearly 11 times the trend. By 2025, the peak was only about 1.2 times the trend.

That may reflect Bitcoin’s maturation as an asset. It may also indicate that the model has begun to overestimate future growth.

How Plausible Is a $1 Million Bitcoin Price?

Rather than a dependable price target, the Power Law serves more as a useful long-term benchmark.

Its biggest accomplishment is that it has identified a comparatively stable growth pattern over more than 15 years of unusually volatile Bitcoin trading.

A fundamental question remains unanswered, however: does an enduring economic relationship make Bitcoin follow this curve, or does the curve merely describe what occurred during Bitcoin’s extraordinary early adoption?

When projecting 10 or 20 years ahead, that distinction matters a great deal.

The $1 million forecast for 2033 fits the model mathematically. Whether Bitcoin reaches that level will hinge on the growth pattern persisting.