BTC To Retire

Bitcoin Power Law Model

A long-run descriptive model for Bitcoin price, used here as one planning input rather than a forecast.

Model

Price as a function of time since genesis

The Bitcoin Power Law, associated with Giovanni Santostasi, fits Bitcoin's historical price against days since the genesis block. It is useful for seeing where spot price sits relative to a long-run trend, but it should not be treated as a promise about future price.

Price = A ร— daysn

A = 3.10ร—10โปยนโท, n = 5.690 ยฑ 0.005. Source: Santostasi & Perrenod, April 2026. Reported fit: Rยฒ = 0.961, ฯƒ = 0.302 dex across 5,696 daily observations.

Centerline Today

โ€”

Spot vs. Trend

โ€”

Projection Calculator

Pick a year and percentile band.

Projected Bitcoin Price

$XXX,XXX

Current Price Loading...
Projected Multiple -
Annual Growth Rate -

Percentile Bands

The calculator uses simple multipliers around the model centerline to avoid pretending there is a single precise future price.

25th

0.55x

Conservative

35th

0.65x

Moderate

50th

0.75x

Median

75th

0.85x

Optimistic

Power Law Visualization

Historical model path, future projection, and percentile bands on a log scale.

Model Health

The useful version of this page is honest about what would weaken or invalidate the model.

Descriptive, not predictive

"Not a predictive law at all but rather a descriptive, curve-fit calculation overlaid atop data."

Attributed to Giovanni Santostasi per Protos, November 2024.

Falsification thresholds

  • Sustained breach of the lower band would weaken the model.
  • A permanent multi-cycle structural deviation would require a refit or retirement.
  • Out-of-sample failure over several future halvings would falsify the recursive-feedback claim.

Substantive critiques

  1. Log price and log time may create spurious regression concerns.
  2. The mechanism is debated; the fit is stronger than the causal story.
  3. Wide bands can make the model hard to falsify in practical use.
  4. Similar fits have been claimed for other cryptoassets, reducing Bitcoin-specific explanatory power.

Rebuttals

  1. Defenders argue log-time is deterministic, so classic cointegration objections are category errors.
  2. Residual-stationarity arguments are used to defend the fit.
  3. The model remains useful as a rough trend frame when paired with stress tests and confidence bands.

Alternative Parameterizations

Other approaches try to address the critique that calendar time is an arbitrary clock.

Calendar Time

In use

Price = A ร— tn

  • A: 3.10 ร— 10โปยนโท
  • n: 5.690 ยฑ 0.005
  • Rยฒ: 0.961
  • Clock: days since 2009-01-03

Activity-Warped Time

Research

Price = a ร— ฯ„b

  • Uses volume or volatility as warped activity.
  • Reported walk-forward improvement in 2026 research.
  • Harder to package into a simple static calculator.

Block-Height Anchor

Research

log(MarketCap) = a + k ร— log(BlockHeight)

  • Uses Bitcoin's native clock.
  • Removes arbitrary calendar start-date choices.
  • Exponent k is not broadly public.

Practical Use

How this app uses the model without pretending it is certainty.

Where it helps

  • Frame long-horizon retirement and accumulation scenarios.
  • Compare spot price with a historical trend band.
  • Use percentiles instead of a single future-price answer.

Where it fails

  • It cannot account for major regulatory, custody, protocol, or market-structure changes.
  • It should not replace Monte Carlo, sequence-risk tests, or tax-aware planning.
  • It should be reassessed when actual market behavior diverges from the band for long periods.

This calculator is for educational purposes only and doesn't represent financial advice. You might want to consult with financial and tax professionals before making decisions.