What this Bitcoin power law calculator shows
The Bitcoin power law is the observation that, on a chart where both axes are logarithmic, Bitcoin’s price since 2010 has scattered around a straight line drawn against the number of days since the genesis block (3 January 2009). This Bitcoin power law calculator evaluates that line — the model’s trend or “fair price” — for any date, with bands one and two standard deviations either side, and tells you when the trend line crosses a price you choose.
The default coefficients are the published fit by physicists Giovanni Santostasi and Stephen Perrenod (Zenodo preprint, version 2, 2 April 2026). You can type your own intercept, exponent and band width to try other fits.
This is a description of past data, not a prediction. A regression line fitted to history carries no guarantee about the future, and it is not financial advice. No prices are fetched; nothing leaves your browser.
How to use the Bitcoin Power-Law Fair Price Calculator
- Keep the default fit, or choose Custom coefficients and type an intercept (log10 A), exponent n and band width σ.
- Pick a date, or press Today.
- Optionally type a price to see how far it sits from the trend, in multiples and in σ.
- Enter a target price to see when the trend line — and the +2σ and −2σ bands — reach it.
- Read the chart and the ten-year table, and copy the result if you need it.
Bitcoin Power-Law Fair Price Calculator features
Published coefficients
Equation (4) of the Santostasi & Perrenod paper: intercept −16.509, exponent 5.690, residual σ 0.302.
Support and resistance bands
Trend × 10±σ and × 10±2σ; ±2σ is the corridor drawn in the paper.
Date for a price
Solves the line backwards: days = 10(log10 P − log10 A) / n.
Log-log chart
Trend, bands, your date, your price and the target on one chart.
Editable model
Every coefficient can be changed, so you can compare fits or test how sensitive the answer is.
The formula and where the numbers come from
The model is log10(price) = log10 A + n × log10(days), which is the same as price = A × daysn, with days counted from 3 January 2009. Santostasi and Perrenod fitted it by ordinary least squares to 5,696 daily US-dollar closing prices from 17 July 2010 to 18 February 2026 and report log10 P = (−16.509 ± 0.009) + (5.690 ± 0.005) × log10 t with R² = 0.961 and a residual standard deviation of 0.302 in log10 units — about a factor of two either way.
Worked example: 1 January 2027 is day 6,572. log10 6,572 = 3.8177, × 5.690 = 21.723, − 16.509 = 5.214, so the trend is 105.214, about $163,600. The ±2σ corridor multiplies that by 10±0.604: roughly $40,700 to $657,200. The trend reaches $1,000,000 when log10 days = 22.509 ÷ 5.690 = 3.956, about day 9,034 — 28 September 2033 on the line, May 2028 on the +2σ band and August 2040 on the −2σ band.
Why it is not a prediction
- A good fit to the past does not prove the relationship will continue. Adoption, regulation and market structure can all change.
- The exponent depends on choices: a May 2026 statistical critique (Baquero and Menezes, arXiv:2605.21316) gets about 5.64 on similar data and shows the exponent moves a lot when the starting date of the day count changes.
- Price has often stayed far from the trend for months or years. The bands describe past scatter, not limits.
- Growth on the trend slows over time: the yearly rate is ((t + 365) ÷ t)n − 1, which falls as t grows.
Related tools
Pair this with the Bitcoin halving countdown, model regular buying with the DCA calculator, or check what a price implies for total value with the crypto market cap calculator.
Bitcoin Power-Law Fair Price Calculator FAQ
What is the Bitcoin power law?
A model in which Bitcoin’s price grows roughly as days since the genesis block raised to a power near 5.7, so its history looks like a straight line on a log-log chart.
How does a Bitcoin power law calculator work?
It counts days from 3 January 2009 to your date, raises that to the exponent and multiplies by the fitted constant, then applies the band width either side.
What is the power-law “fair price” today?
Press Today to see the trend for the current date. It is the centre of the historical scatter, not a value the price must return to.
Which coefficients should I use?
The default is the 2026 published fit. Other analysts use slightly different intercepts and exponents; enter theirs as custom coefficients to compare.
Can the power law predict Bitcoin’s price?
No model can promise that. The power law is a historical regression with no predictive guarantee, and this page is not investment advice.