A power-law model based on Bitcoin’s age puts its trend price near $1 million by 2033, while suggesting that growth will slow as the network matures. Physicist Giovanni Santostasi developed the model, but its close fit with past prices does not mean it can accurately predict future ones. The 2033 figure is a mathematical estimate, not a dependable price target.
How the model links Bitcoin’s age and price
A power law describes a mathematical relationship in which one quantity changes according to a fixed exponent. The concept has been used in fields including physics, the natural sciences and economics, with roots stretching back centuries. Early examples include work by astronomer Johannes Kepler.
Santostasi observed that Bitcoin’s early price history appeared to follow a similar pattern: the asset continued to gain value over time, but its growth rate declined as it aged.
Under the model, each doubling of Bitcoin’s age corresponds to an roughly 50-fold increase in its long-term trend price. For example, if an asset’s trend price were $1,000 at age 10, the model would put it at $50,000 at age 20 and $2.5 million at age 40. The second 50-fold increase takes 20 years, compared with 10 years for the first, reflecting the model’s assumption of slower growth over time.
One possible explanation is the network effect: as adoption expands, Bitcoin’s network may become more valuable, which could be reflected in its long-term price curve. Whether network growth has a stable, lasting causal relationship with price remains central to the question of whether the model can be extended into the future.
Strong historical fit is not forecast accuracy
Santostasi and Stephen Perrenod published a peer-reviewed study in 2026 examining the relationship between network adoption and Bitcoin’s price. It used 5,696 daily Bitcoin price observations from July 2010 through February 2026. The model explained about 96% of the variation in historical log prices.
That figure measures how closely the model fits past data; it does not mean the model has a 96% price-forecast accuracy rate. Historical observations can show how well a curve describes the past, but cannot establish on their own that prices will continue to follow the same pattern.
Independent researchers at a university in Portugal also found that, among the models they tested, a simple power law performed relatively well in forecasting prices over the next 12 to 24 months. However, they questioned whether the mathematical relationship is stable or fundamental. Its relative performance in short-term forecast tests does not prove that it will hold over a longer horizon.
Bitcoin’s bull-market peaks have moved closer to the trend line
The power-law trend has not captured the full range of Bitcoin’s bull-market swings. Past cycle peaks have been well above the model’s trend line: the 2013 peak was close to 11 times the trend price, while the ratio was about 1.2 times in 2025.
The narrowing gap could reflect a maturing Bitcoin market and more contained price swings. It could also indicate that the model is beginning to overstate future growth. Historical differences alone do not establish which explanation is more likely.
The estimate of about $1 million by 2033 follows only if the power-law relationship continues. The model is best viewed as a reference point for considering long-term trends, rather than a firm price target. Changes in Bitcoin adoption, market structure or its growth pattern could make the projection inapplicable.