Bitcoin Power Law Calculator

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Reviewed by: David Chen, CFA. This calculator helps model long-term Bitcoin price behavior based on the logarithmic Power Law framework.

Use the Bitcoin Power Law Calculator to project future price targets or determine the required scaling factor and exponent based on historical data points.

Bitcoin Power Law Calculator

The Solved Variable is:

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Bitcoin Power Law Calculator Formula

$$P = A \cdot T^B$$

Formula Source: The Power Law model is widely discussed in crypto analysis, notably by researchers like this study and this detailed analysis.

Variables Explained

The Power Law equation $P = A \cdot T^B$ involves four primary variables that you can use the calculator to solve for:

  • Price (P, USD): The resulting or target Bitcoin price in US Dollars.
  • Days from Genesis (T): The total number of days that have passed since the Bitcoin genesis block (January 3, 2009). This represents Time.
  • Scaling Factor (A, Constant): A fixed constant value derived from historical price action, determining the magnitude of the power law curve.
  • Power Law Exponent (B): The rate at which the price changes with respect to time, often considered a crucial, stable constant in this model (typically 4.8).

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What is the Bitcoin Power Law?

The Bitcoin Power Law model posits that Bitcoin’s long-term price movement, when plotted on a log-log scale, follows a remarkably linear path. This suggests that price growth is non-exponential (not a constant percentage gain) but rather follows a consistent, predictable decay rate relative to time. This linearity across multiple orders of magnitude is characteristic of power law functions.

The primary significance of this model lies in its ability to smooth out short-term market volatility and highlight the underlying long-term trend. The model suggests that the rate of return decreases as the asset matures, but the absolute price continues to rise predictably over decades. It is often used by long-term investors to establish lower and upper bounds for Bitcoin’s price trajectory.

While powerful, the model is a descriptive framework, not a guaranteed prediction tool. It assumes the continuation of current market dynamics and does not account for black swan events, regulatory changes, or fundamental technology shifts.

How to Calculate the Power Law Price (Example)

Here is a step-by-step example for solving the Price (P) variable:

  1. Determine the Inputs: Assume you have a target Day Count (T) of 6,000, a stable Scaling Factor (A) of 0.00000004, and a Power Law Exponent (B) of 4.8.
  2. Apply the Formula: Substitute the known values into the equation: $P = 0.00000004 \cdot (6000)^{4.8}$
  3. Calculate Time’s Power: First, raise the Days from Genesis (6,000) to the power of the Exponent (4.8). The result is approximately $5.21 \times 10^{17}$.
  4. Multiply by the Scaling Factor: Multiply this result by the Scaling Factor (0.00000004): $P = 0.00000004 \cdot 5.21 \times 10^{17}$
  5. Final Result: The calculation yields a target Price (P) of approximately $20,840,000 USD$.

Frequently Asked Questions (FAQ)

  • What is the typical value for the Power Law Exponent (B)?

    Historically, the exponent has been observed in the range of 4.8 to 5.5, with 4.8 being a commonly referenced value that fits most long-term data sets well. However, this value may shift slightly over time.

  • Is the Bitcoin Power Law better than Stock-to-Flow?

    They are different models. Stock-to-Flow focuses on scarcity and supply reduction (halvings), while the Power Law focuses on time progression and market maturity. The Power Law has historically shown a lower price ceiling and floor, providing a potentially more conservative long-term trend line.

  • What happens if the inputs are mathematically inconsistent?

    If you input values for all four variables and they do not satisfy the equation $P = A \cdot T^B$, the calculator will flag an “Inconsistency Detected” error. This indicates that the chosen set of inputs does not fit the Power Law model.

  • What is the Genesis Block date?

    The Bitcoin Genesis Block was mined on January 3, 2009. The “Days from Genesis” variable (T) is calculated from this date.

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