Model: price ≈ 1.0117×10⁻¹⁷ × (days since genesis)^n · Santostasi (2018). Historical prices are yearly USD averages. Educational only — not financial advice.
What the power law is
The Bitcoin Power Law is a mathematical model that describes how Bitcoin’s price has tracked the passage of time since the Genesis block was mined on January 3, 2009. The relationship is a power law: price scales with elapsed days raised to an exponent. In plain terms, every time the number of days doubles, the expected price rises by a predictable multiplier — one set by the exponent. This is distinct from, say, an exponential growth model, which compounds at a constant percentage per period regardless of starting point.
The model is written: price ≈ A × (days since genesis)^n, where A is a calibration coefficient and n is the exponent. The key insight is that on a log-log chart — with logarithmic axes for both price and time — a power law plots as a straight line. Bitcoin’s price history, through booms and crashes, has broadly tracked such a straight line over fifteen years of data.
This relationship was formally described and shared by Giovanni Santostasi, a physicist, who published his work from 2018 onward showing that Bitcoin’s price fits a power law over multiple orders of magnitude of price. Harold Christopher Burger independently published related analysis in 2019, framing it as a “long-term power law corridor of growth.” Both researchers emphasized that the model is descriptive of past data — a fit to observed history — not a mechanistic prediction about future prices.
What the model produces is a corridor: a support band below which Bitcoin has historically rarely traded for extended periods, a fair-value centre line representing the regression midpoint, and a resistance band above which Bitcoin has historically not sustained prices for long. The corridor expands over time because the exponent amplifies small changes in elapsed days into large changes in expected price.
The three exponents and what they represent
This tool uses three exponents, each defining one band of the power law corridor:
Support — n = 5.55: The lower boundary of the corridor. Historically, Bitcoin has not spent extended periods below this line. When the price dips into support territory, it has tended to revert upward over subsequent months to years. The support band is relevant as a long-term accumulation reference: not a guarantee, but an approximate floor that has held across four full market cycles.
Fair value — n = 5.82: The regression centre. This is the exponent that minimises the sum of squared residuals when you fit Bitcoin’s yearly price history on a log-log scale. It sits between the support and resistance bands. When Bitcoin’s price is close to the fair-value line, the model says the asset is neither historically cheap nor historically expensive relative to where it has spent most of its history. Giovanni Santostasi uses this exponent as the centrepoint of his model.
Resistance — n = 6.05: The upper boundary. Bitcoin has historically marked major market tops when it approached or briefly touched the resistance band. The most prominent examples are the December 2017 top (the first time Bitcoin approached this band at scale) and the late-2021 peak. After touching resistance, Bitcoin has historically reverted sharply toward fair value and then support. The resistance line is not a target or ceiling — it is a historical observation about where buyer exhaustion has tended to occur.
The three lines together form a zone. A Bitcoin price inside that zone is “within the model.” A price far above resistance represents an unusual extension; a price far below support represents an unusual compression. Both have historically resolved over multi-year timescales.
Why the power law might work
There is no law of physics that requires Bitcoin to follow a power law. But several phenomena associated with network growth and adoption produce power-law-like dynamics in practice:
Metcalfe’s Law and network value. Metcalfe’s Law states that the value of a communications network is proportional to the square of its number of users. Bitcoin is a monetary network, and while it doesn’t follow Metcalfe’s Law exactly, its value is plausibly proportional to some function of the number of participants. As Bitcoin’s user base has grown — from a handful of cypherpunks in 2009 to tens of millions of addresses by the mid-2020s — the network’s value has grown at a pace consistent with a power of adoption.
S-curve adoption and time. Technology adoption follows S-curves: slow start, accelerating middle, and eventual saturation. The number of new Bitcoin participants added each year has broadly grown as a power function of time, not a constant or exponential. Power-law price growth is what you’d expect from a network whose adoption itself follows a power-law trajectory.
Hash-rate scaling. Bitcoin’s mining hash rate has also followed a power-law trajectory since 2009. Because hash rate is linked to security, security to confidence, and confidence to demand, the chain of relationships plausibly anchors price growth to hash-rate growth — and hash rate grows as a power of time.
Self-similarity across cycles. Bitcoin has experienced four major bull-bear cycles. Each cycle’s peak and trough have sat within the power law corridor. This consistency across qualitatively different market regimes — different mining hardware generations, different regulatory environments, different institutional involvement — is what gives proponents confidence that the model may reflect something structural about Bitcoin’s monetisation trajectory.
Why the power law might NOT work
Being honest about a model’s limitations is as important as explaining what it gets right.
Small sample size. Bitcoin is fifteen years old as of 2025. Fifteen years is four market cycles and perhaps three doublings of the Bitcoin halving schedule. Fitting a regression line to fifteen data points on a log-log scale and projecting it to 2050 involves enormous extrapolation risk. Statistical confidence intervals grow dramatically over the forecast horizon. What looks like a tight corridor in historical data could widen to orders of magnitude of uncertainty by 2040.
A unique monetisation phase. Bitcoin may be in a once-in-history phase of monetary adoption — a transition from zero to global reserve asset status. If so, the dynamics of this phase are unlike anything that will occur afterward. The power law exponent may shift dramatically once adoption saturates, or if Bitcoin fails to achieve broad monetary adoption, the model simply fails entirely.
No mechanism forces this. A power law fit is a curve fit. There is no guarantee that the forces that produced the historical curve will continue. Regulatory prohibition in major economies, a critical protocol vulnerability, the emergence of a superior competitor, or any number of macro shocks could invalidate the model completely. A straight line on a log-log chart is not a physical constant.
Selection bias. Researchers examining Bitcoin’s price history are looking at a survival success — a monetary network that survived. Many other cryptocurrency and monetary network experiments have failed and would not show a clean power law. The selection effect of studying only Bitcoin means the model reflects the world’s most successful example of this phenomenon, which may not generalise.
Step-function realities. Bitcoin halvings — programmatic supply reductions that occur roughly every four years — introduce discrete step-changes in the supply issuance schedule. The power law model treats price growth as smooth and continuous, but halvings create discrete shifts in miner revenue, supply-side selling pressure, and market sentiment. Whether halvings are “priced in” gradually or produce acute price responses is debated; either way, the smooth model is a simplification of a reality with known discontinuities.
How to use this tool responsibly
This tool is appropriate for one purpose: building long-term intuition about the scale of Bitcoin’s historical price growth and where current prices sit relative to the model’s historical corridor.
It is not appropriate for: timing purchases or sales, sizing positions, managing risk, or making any financial decision. The model cannot tell you whether Bitcoin will be higher or lower in six months, two years, or even a decade. Market prices can and do diverge from any model for extended periods, including for periods longer than most investors’ patience.
Responsible use means:
- Using the model as a rough long-term reference, not a precise target
- Remembering that the corridor will continue to expand — the range of outcomes it implies grows wider over time, not narrower
- Treating any year’s fair-value estimate as a rough central tendency with enormous uncertainty bounds
- Never treating this as financial advice, which it is not
FAQ
Is this financial advice?
No. This tool is for educational and informational purposes only. The Bitcoin Power Law is a descriptive statistical model, not investment guidance. Past price behaviour does not guarantee future results. Consult a qualified financial advisor for personal investment decisions.
Where does the coefficient come from?
The coefficient A (approximately 1.0117 × 10⁻¹⁷ in this tool) is determined by calibrating the model so that the fair-value line passes close to observed historical yearly average prices. In a more rigorous regression, you would fit A and n simultaneously via ordinary least squares on log-transformed price and log-transformed days. The value used here is calibrated to place the fair-value line at approximately $84,000 for January 2025, consistent with Bitcoin’s actual price range during that period.
What happens at the next halving?
The model assumes smooth, continuous price growth as a function of elapsed time. Halvings — occurring approximately in 2028, 2032, 2036, and 2040 — are not explicitly modelled. In practice, halvings may cause the price to front-run the model’s corridor in the months before and after the event. The model provides no guidance about the timing or magnitude of halving-related price movements, only about the broad trajectory over multi-year time horizons.
Can the power law break?
Yes. Any of the following would invalidate the model: a fundamental Bitcoin protocol failure, regulatory prohibition in major economies, saturation of the addressable user base, or simply a change in the underlying adoption dynamics. The model has held over four cycles and fifteen years; it may not hold over the next fifteen. Use accordingly.
What is the difference between support and resistance in this context?
In this model, “support” and “resistance” are not dynamic chart levels as used in technical analysis — they are the lower and upper boundaries of the historical power law corridor. Support is the line below which Bitcoin has historically traded very rarely and briefly. Resistance is the line above which Bitcoin has historically peaked and reversed. Both are statistical observations about where Bitcoin’s price has historically spent its time.
Primary sources:
- Giovanni Santostasi — Power Law model and ongoing research: giovannisantostasi.medium.com
- Harold Christopher Burger — “Bitcoin’s Natural Long-Term Power-Law Corridor of Growth” (2019): medium.com/@hcburger1/bitcoins-natural-long-term-power-law-corridor-of-growth-649d0e9b3c94
- Bitcoin Genesis block: Block 0, mined January 3, 2009 — verifiable on any Bitcoin block explorer