Power Law Bitcoin Calculator
Learn about the time-based Power Law model. The table below is a separate hypothetical 35% compound-growth example, not a Power Law forecast.
Hypothetical 35% Compound-Growth Scenario
Current BTC price: Loading... · Assumed growth: 35% per year
| Year | Hypothetical Value | Growth from Today |
|---|---|---|
| 2028 | — | — |
| 2030 | — | — |
| 2035 | — | — |
| 2040 | — | — |
| 2050 | — | — |
Hypothetical fixed 35% annual growth, not a Power Law output. No halvings, volatility, fees, taxes, or inflation. Not financial advice. Returns may be negative.
The full calculator uses different methods: a market-price-anchored time function for Power Law and changing halving-phase rates for Stock-to-Flow, not PlanB’s original regression. Results differ from this fixed-growth example; no retirement date is guaranteed.
What Is the Bitcoin Power Law?
The Bitcoin Power Law is a mathematical model discovered by physicist Giovanni Santostasi that describes Bitcoin's price as a power function of time. Unlike simple exponential models, a power law captures the fact that Bitcoin's growth rate gradually decreases over time — fast in the early years, slower as it matures — while still following a predictable mathematical curve.
When plotted on a log-log scale (logarithmic price vs. logarithmic time), Bitcoin's entire price history from 2010 to today falls remarkably close to a straight line. This linear log-log relationship is the hallmark of a power law. The model has an R² value above 0.95, meaning it explains over 95% of Bitcoin's historical price variance.
For long-term investors and retirement planners, the Power Law provides a mathematically grounded framework for setting expectations. Rather than relying on hype or fear, you can use this model to project where Bitcoin's price corridor is likely to be in 5, 10, or 20 years.
How the Power Law Model Works
Log-Log Linear Regression
The model plots log(price) against log(days since Bitcoin genesis). The resulting near-perfect straight line allows precise extrapolation of future price corridors, accounting for decreasing growth rates as the asset matures.
Time-Dependent Growth
Power Law growth depends on elapsed time since genesis and the chosen exponent. A constant 35% growth assumption is not a Power Law model; it is only an illustration used in the separate table above.
Support & Resistance Bands
The Power Law defines not just a median price but also upper and lower bands. Historically, Bitcoin has never fallen below the lower Power Law support band, making it useful for identifying accumulation zones and overvaluation periods.
Found in Nature & Networks
Power laws appear throughout nature — in earthquake magnitudes, city populations, and network growth. Bitcoin's adherence to this pattern suggests its price is driven by fundamental network adoption dynamics rather than pure speculation.
Hypothetical Fixed-Growth Scenarios
| Scenario | Basis | Annual Growth | 2030 Projection |
|---|---|---|---|
| 35% scenario | Hypothetical fixed growth | 35% assumed | — |
| 40% scenario | Hypothetical fixed growth | 40% assumed | — |
| 25% scenario | Hypothetical fixed growth | 25% assumed | — |
| 20% scenario | Hypothetical fixed growth | 20% assumed | — |
Compare all models side by side in our model comparison tool.
The full calculator uses different methods: a market-price-anchored time function for Power Law and changing halving-phase rates for Stock-to-Flow, not PlanB’s original regression. Results differ from this fixed-growth example; no retirement date is guaranteed.
Frequently Asked Questions
What is the Bitcoin Power Law?
A power law expresses price as a power of time since Bitcoin genesis. It is not constant annual compound growth.
What does the table on this page calculate?
A hypothetical scenario: current BTC price × (1 + 35%) to the power of the number of years. It uses calendar-year differences rather than exact target dates. It calculates neither Power Law nor Stock-to-Flow and does not incorporate halvings.
Why does the full calculator produce different results?
The full calculator uses a market-price-anchored time function for Power Law: 10^−17 × days since January 3, 2009^5.8. Its Stock-to-Flow option uses changing growth rates by halving phase, not PlanB's original regression. It steps monthly using 30.44 days per month. These methods differ from this table's fixed growth.
Are these reliable return forecasts?
No. The table illustrates an assumption without volatility, fees, taxes, or inflation. Bitcoin can lose all its value. Historical patterns do not guarantee future returns. This is not financial advice.
Related Resources
Stock-to-Flow Calculator
Bitcoin scarcity-based price model
Rainbow Chart Bitcoin
Logarithmic regression color bands
Compare All Models
Side-by-side model comparison tool
Power Law Deep Dive
Full article on the Power Law model
Price Predictions 2026–2050
Year-by-year projections from all models
How Much Bitcoin to Retire?
Calculate BTC needed for your expense level