The Bitcoin power law
Bitcoin's price is famously volatile, yet over 17 years it has grown along a remarkably regular path: in proportion to a power of its age.
Today, 5 November 2026 the power-law trend is at $122,000, and Bitcoin trades at $80,545. Live chart
How it works
Take the time since the genesis block, the first Bitcoin block of 3 January 2009, and call it t. Bitcoin's price has grown roughly like
price ≈ a · tn
where the exponent n lies between 5 and 6. Doubling Bitcoin's age has multiplied its trend price by about 25.5, roughly 45 times.
On an ordinary chart this is a curve that bends ever upward. Draw both axes logarithmically, price and time, and a power law becomes a straight line. That is why the chart on our main page is drawn log–log: the trend is the straight dashed line, and the price swings around it.
Why a power law?
The power law was discovered by the physicist Giovanni Santostasi, creator of the Power Law Theory of Bitcoin. In his theory, the number of Bitcoin addresses grows roughly with the cube of time, and the price grows with the square of the number of addresses, a network effect similar to Metcalfe's law. Together that gives about the sixth power of time. More on his site: bitposeidon.com.
Power laws appear throughout nature, wherever growth feeds on itself without a fixed time scale: city sizes, earthquakes, the growth of networks.
What it means for the future
A power law slows down in relative terms. Each further doubling of the price takes longer than the last, because the price follows Bitcoin's age, and age grows linearly. The trend:
| End of | Power-law trend |
|---|---|
| 2028 | $224,000 |
| 2030 | $372,000 |
| 2035 | $1,110,000 |
| 2040 | $2,730,000 |
The trend is not the price. Bitcoin moves in four-year cycles around it, driven by the halvings, rising far above the trend and then falling below it. Our fair value adds this cycle to the trend, and the price prediction shows the result year by year.
Questions
What is the Bitcoin power law?
The observation that Bitcoin's price has grown roughly in proportion to a power of its age: price ≈ a · tn, with t the time since the genesis block and n between 5 and 6. On a chart with both axes logarithmic it is a straight line.
Who discovered the Bitcoin power law?
The physicist Giovanni Santostasi, creator of the Power Law Theory of Bitcoin. More on his site, bitposeidon.com.
Where is the power law today?
The power-law trend is at $122,000 today (5 November 2026). Bitcoin trades at $80,545, 66% of the trend.
Does the power law predict the price?
It describes the long-term trend, not the price on a given day. The price has spent years well above and below it. Our fair value adds the four-year halving cycle on top of the trend.
Model estimates, not a promise: past behaviour is no guarantee for the future. Not financial advice.