Bitcoin Power Law
A long-term model for understanding Bitcoin's historical growth path.
Educational model only. Not financial advice. Not a price guarantee.
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Reading the model
Every figure below is an estimate from the canonical power-law model line. They describe a long-term pattern, not the future.
How to read this chart
Real historical price data. It stops at the latest available point.
The canonical long-term power-law trend line (Bitbo / BGeometrics coefficients).
Mathematical estimates that continue to 2040. Not predictions.
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What is the Bitcoin Power Law?
It is a simple model that compares Bitcoin's price to how much time has passed since it launched in 2009. Plotted on a special log scale, Bitcoin's long history has roughly followed a straight line.
That line is an attempt to describe Bitcoin's historical long-term growth pattern — a smooth trend underneath all the booms and crashes — and it can help investors zoom out from day-to-day volatility.
On the chart, the orange Bitcoin price line stops at the latest real data. The fair value and band lines then extend forward only as mathematical estimates — shown dashed and faded, with a Today marker at the boundary. Those future bands are not predictions of where Bitcoin will trade.
And it is not guaranteed to keep working. It is a pattern from the past, captured by a fixed published formula — a model that can fail, not a law of nature and not a forecast.
The Story Behind the Bitcoin Power Law
Where the model came from, why people follow it, and the criticisms worth knowing. Background, not endorsement.
Who is Giovanni Santostasi?
Giovanni Santostasi is a physicist and data scientist who helped popularize the idea that Bitcoin's long-term price tracks a power law of time. He has written and spoken widely on the subject, framing Bitcoin's growth with the same mathematics that describes power-law behavior in physics and complex systems. He is an educator and commentator on this model, not an investment adviser.
How the model was developed
The observation that Bitcoin's price versus time forms a straight line on log-log axes predates any single author. Analyst Harold Christopher Burger described a "power-law corridor" in 2019. Santostasi formalized the relationship as price ≈ A · daysn with an exponent near 5.8, and argued it reflects feedback between adoption, network effects, and mining difficulty rather than a curve fitted for its own sake. The fair-value line on this page uses the canonical coefficients published through Bitbo and BGeometrics.
Why investors follow it
Supporters value it as a long-horizon lens. It smooths over violent cycles, offers an estimated fair-value corridor instead of a single number, and has historically stayed within its bands across several boom-and-bust cycles. Its inputs are unusually simple, essentially just elapsed time, which makes it easy to chart and reason about.
Important limitations and criticisms
- It is fitted to the past. Nothing forces the relationship to continue.
- Critics note that many growth series look linear on log-log axes, so the straight line may be less meaningful than it appears.
- It models time alone, not demand shocks, regulation, liquidity, macro conditions, or competition.
- Extended far enough it implies ever-rising prices, which critics consider implausible.
- Like any single model it risks overfitting and survivorship bias. A different popular model, stock-to-flow, broke down after 2021.
Why it remains popular despite limitations
Even skeptics acknowledge the model has tracked price across multiple cycles with a single, transparent formula. Its simplicity, its long-term framing, and its visibility on widely used dashboards keep it in circulation, especially after more complex models lost credibility. It is best treated as one historical lens among many, never a promise.
Go deeper on the researcher behind the model, his background, and his contributions.
Giovanni Santostasi: biographySources: CCN interview, Samara Asset Group, Bitbo / BGeometrics.
How investors can think about it
- Use it as one lens, not the only lens. It is context, not a signal to buy or sell.
- Watch for extreme deviations — prices far above resistance or far below support have historically been unusual.
- Compare the current price to the long-term trend, rather than to last week's price.
- Combine it with risk management: position sizing, diversification, and a time horizon you can hold through.
- Never invest based on one model alone. Any single model can be wrong.
Important limitations
- This model is based on a formula fitted to past Bitcoin prices.
- It can break if Bitcoin's market structure changes.
- It does not account for regulation, liquidity, macro shocks, custody risk, or investor behavior.
- It should be used as one lens, not the only lens.
- It is not financial advice.
Source & model transparency
- Price history source
- Blockchain.com
- Model type
- Log-log power law (canonical coefficients)
- Coefficients
- a = 5.8451542, b = -17.0161223
- Model source
- Bitbo / BGeometrics (Santostasi power law)
- Corridor
- Support & resistance run parallel to the trend (canonical envelope)
- Projection horizon
- 2040
- Current price
- Latest available historical point, not a live quote
Related resources
Educational content only. The Bitcoin Power Law shown here is a model of past behaviour fitted to historical price data. Fair value and band figures are estimates, not forecasts or guarantees. This page is not financial advice or a recommendation to buy or sell any asset. Always do your own research and consider speaking with a licensed financial professional.