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Bitcoin power law
The Bitcoin power law is the finding that bitcoin's price has followed a roughly straight line when both price and days since the genesis block are drawn on log scales, which means price has grown like days raised to a fixed power. On our fit that power is about 5.59, and today's line sits at $142,669 against a price of $74,317. It is a fit to history, not a forecast and not advice.
log10(price) = 2.4297 x ln(days since January 3, 2009) - 16.1849
The same fit as a power law: price = 10-16.1849 x days5.595. On log-log axes it is a straight line.
What Is the Bitcoin Power Law
The Bitcoin power law is a model in which price grows in proportion to time raised to a fixed power, with time counted in days since the genesis block on January 3, 2009. A power law looks like a straight line when both axes use a log scale, and bitcoin's daily closes since 2010 have stayed near such a line.
The model says nothing about why. It describes the shape of sixteen years of price data with two numbers: the power, called the exponent, and a constant that sets the height of the line.
Bitcoin Power Law Chart Today
On the Bitcoin power law chart today, the price of $74,317 sits against a fitted line at $142,669. The chart draws both axes on log scales, so the line is straight, and it marks how far today's price is from it.
The line is the same one that runs through the middle of our Bitcoin rainbow chart, drawn on a different time axis. The rainbow uses calendar dates; this chart uses the log of days since the genesis block.
How Our Fit Becomes a Power Law
Our fit becomes a power law with one line of algebra, because a log of days in any base is a log of days in base 10 times a constant. The fit is log10(price) = 2.4297 x ln(days) - 16.1849, a least squares fit over every daily close since August 18, 2010 from the Blockchain.com price series, frozen on November 8, 2026.2 The steps:
- Swap the natural log for base 10: ln(days) = 2.3026 x log10(days).
- Multiply: 2.4297 x 2.3026 = 5.5946, so log10(price) = 5.5946 x log10(days) - 16.1849.
- Raise 10 to both sides: price = 10^-16.1849 x days^5.5946.
- Round: price is proportional to days raised to about 5.59.
So doubling the days since genesis multiplies the fitted price by 2 to the power 5.59, about 48 times. Each year adds a smaller share of days than the last, which is why the line bends flatter on a calendar chart.
The Published Bitcoin Power Law Model
The published Bitcoin power law model has several authors; a 2026 arXiv paper calls the work of Giovanni Santostasi and Perrenod the most recent formal account, and reports an exponent of 5.690 over July 18, 2010 to February 18, 2026, according to a 2026 arXiv paper by Baquero and Menezes that tested the model.3
An earlier version came from Harold Christopher Burger, who in 2019 described a power-law corridor around the price, with a slope of about 5.845 on all data and about 5.029 fitted to market tops alone.4 A power law calculator credited to Burger and Santostasi uses 5.84509376 with corridor lines at about 4 times and 0.25 times its fair value.
Our Exponent Versus the Published Ones
Our exponent of about 5.59 sits below the published full-history fits, which run from 5.644 to 5.845 depending on the data window and the method, and above the 5.029 slope Burger fit to the tops alone. The numbers differ, and the table lays them side by side.
Small gaps in the exponent become large gaps in price over time. On November 8, 2026, the 5.845 calculator formula sat about a third above our line. Baquero and Menezes found the exponent shifts with the choice of time origin, so a different start date alone moves it.
| Fit | Exponent | Data window |
|---|---|---|
| Onchain Wiki (frozen November 8, 2026) | 5.59 | August 18, 2010 to November 8, 2026 |
| Baquero and Menezes (arXiv, 2026) | 5.644 | August 18, 2010 to March 25, 2026 |
| Santostasi and Perrenod (2026), as reported | 5.690 | July 18, 2010 to February 18, 2026 |
| Burger corridor (2019), all data | 5.845 | as published in 2019 |
| Burger corridor (2019), tops only | 5.029 | market tops |
Power Law Limits: Not a Forecast
A power law has limits as a price model: it is a fit to past prices, and it is not a forecast. Baquero and Menezes call the evidence for a true structural law weak, even though in their tests the simple power law forecast better than more complex curves over 12 to 24 months.
Price has spent long stretches far from the line, above it in every cycle top and below it at every low; the 4 year cycle chart shows those swings. A line drawn through history can stop fitting at any time, and nothing on this page is advice.
Questions People Ask About Bitcoin power law
These are the questions people ask next about Bitcoin power law.
What is the Bitcoin power law formula?
The Bitcoin power law formula is price = A x days^n, with days counted from the genesis block on January 3, 2009. Published fits put n between 5.644 and 5.845; our fit gives about 5.59 with A about 6.53 x 10^-17.
Who created the Bitcoin power law?
The Bitcoin power law has more than one author: Harold Christopher Burger published a power-law corridor version in 2019, and a 2026 arXiv paper calls the work of Giovanni Santostasi and Perrenod the most recent formal account. Santostasi's 2026 paper with Perrenod reports an exponent of 5.690.
Is the power law the same as the rainbow chart?
The power law and our rainbow chart use the same line: our rainbow fit is a power law with exponent about 5.59, drawn on a calendar axis with nine bands around it. Other rainbow charts use their own formulas, and Blockchaincenter's current one also fits a power law.
Does the power law predict bitcoin's price?
The power law does not predict bitcoin's price with any certainty; it describes how past prices lined up. Researchers testing it found it forecast reasonably over 12 to 24 months in the past, but they call the case for a true law weak.
Sources
Every number on this page comes from these sources, checked November 10, 2026.