Bitcoin Power Law Chart
See Bitcoin's price against its long-run power-law trend on a log scale, with support and resistance bands and how far today's price sits above or below model fair value. No signup, runs in your browser.
Model: price ≈ 10-16.16 × days5.60, where days is the number of days since the Bitcoin genesis block (Jan 3, 2009), fit by linear regression on a log-log scale.
How to Read the Power-Law Chart
- 1The orange line is the fitted power-law fair value; the blue line is Bitcoin's actual price.
- 2Both axes are effectively logarithmic, so the long-run trend appears as a near-straight line.
- 3The shaded band marks the corridor cycle tops and bottoms have historically reached.
- 4The deviation readout tells you how far current price sits above (overvalued) or below (undervalued) the model.
Why a Power Law, Not an Exponential
Most assets are discussed in terms of a percentage growth rate, which is exponential — a straight line only when price is plotted on a log axis against linear time. Bitcoin is unusual because it forms a straight line when both price and time are logarithmic. That is the signature of a power law: price rising as time raised to a fixed exponent (empirically around 5.8). One intuition is that Bitcoin's adoption, network effects, and security budget have all grown as power laws of time, and price has tracked them. Whatever the cause, the fit across more than a decade and several 100× ranges is what makes the model interesting.
The practical read is relative, not absolute. When price pushes into the upper band far above the fair-value line, the model is telling you the market is historically stretched; when price sinks toward the lower band, it has historically been closer to a generational low. It said nothing useful about the exact top or bottom date — only about how extended things are. And the honest caveat is that a power law is a curve fit to the past: it has held so far, but four cycles is a small sample, and models like this tend to work right up until they don't. Use it as a long-horizon compass alongside tools like the halving countdown and cycle predictor, not as a trading trigger.
Understanding the Model
Straight line on log-log
The whole idea is that price versus time is a straight line when both are logarithmic. If that line ever bends persistently, the power-law relationship is breaking down.
Deviation beats price
The useful number is not the price itself but how far it sits from fair value. A big positive deviation signals froth; a big negative one signals historically cheap.
Bands are descriptive
The support and resistance corridor comes from where past cycles peaked and bottomed relative to the line. They describe history — they are not hard floors or ceilings.
It ignores timing
The model says how stretched price is, never when it will revert. Price can ride the upper band for months or sit below the line through a long winter.
Small sample, real risk
The fit rests on roughly four cycles. That is enough to be striking and not enough to be certain. Every long-run model carries the risk that the pattern simply ends.
Pair it with cycle tools
The power law gives the long-horizon backdrop; the halving countdown and cycle predictor add the four-year rhythm. Together they frame context better than any one alone.
Frequently Asked Questions
What is the Bitcoin power law?
The Bitcoin power law is a model observing that Bitcoin's price has, over its whole history, tracked a straight line when both price and time are plotted on logarithmic axes. Mathematically, price ≈ A × (days since genesis)^n. This means price grows as a power of time rather than exponentially, producing a long-run trend line that the actual price oscillates above and below across cycles.
How is the model on this page calculated?
The tool takes a set of historical BTC prices spanning 2011 onward, converts both price and the number of days since the January 2009 genesis block to log scale, and fits a straight line by ordinary least-squares regression. The slope of that line is the power-law exponent and the intercept sets the level. The fitted line is then projected across the full time range and compared with the current price.
What do the support and resistance bands mean?
The dashed bands above and below the central model line mark a rough corridor that price has historically stayed within — roughly the fair-value line multiplied by about 0.4 at the bottom and about 2.9 at the top. Bull-market peaks have tended to reach the upper band and bear-market bottoms the lower band. They are descriptive guides drawn from past behaviour, not guaranteed limits.
Does the power law predict future Bitcoin prices?
No. The power law is a description of the past that some use as a long-term reference, not a forecast. It has held remarkably well so far, but any model fit to historical data can break — through regulation, a structural change in adoption, or simply the pattern ending as the market matures. Treat the fair-value line as context for how stretched price is, never as a promise of where it will go.
Why use a logarithmic scale?
On a normal linear scale, Bitcoin's early history is an invisible flat line and only recent prices are visible, which hides the trend. A logarithmic price axis gives equal visual weight to each 10× move — from $1 to $10 looks the same as $10,000 to $100,000. That is what makes the power-law relationship appear as a straight line and lets you see the whole history at once.
Is the current price live?
The current BTC price is fetched from a public market API when the page loads, and is compared against the model's fair value for today to show the deviation. The historical trend line is built from an embedded dataset, so the chart renders even if the live price is unavailable. Nothing you do is stored or sent anywhere.