The Bitcoin Power Law Explained: The Model Behind the Long-Term Trend

The Bitcoin Power Law is a model that explains Bitcoin's price with a single variable: the time since the network started on January 3, 2009. That gives you a line, the Power Law line. At 42 % of this line sits the floor, where almost every crash has ended so far. Above it lies the long-term trend, the "fair value". The model shows whether Bitcoin is cheap or expensive today, not tomorrow's price.

Why you need a model for Bitcoin

Bitcoin sometimes falls by 70% or more, then climbs to new highs again. If you only watch the daily price, you tend to buy in euphoria and sell in panic. That is exactly what costs long-term holders the most money.

A model gives you a yardstick. It doesn't say what happens tomorrow. It says whether today's price is high or low measured against Bitcoin's entire history. With that yardstick you can decide more calmly: keep saving, buy more or simply hold.

What is the Bitcoin Power Law?

A "power law" means the price grows with a fixed power of time. When Bitcoin's age doubles, the model's line, the Power Law line, rises roughly 50-fold.

That sounds abstract, but it has a simple consequence: the older Bitcoin gets, the more slowly this line grows in percentage terms. In 2011 it still grew tenfold within a year. Today it rises by a little over a third a year, and that figure keeps falling.

That sets the Power Law apart from models with exponential growth, which assume a constant return. The Power Law expects growth that weakens year after year.

The lines you see on bitcoin-powerlaw.com are built on this line: the floor as a fixed share of the line, and above it the trend, the fair value.

What the Power Law looks like on a log chart

On a normal chart, Bitcoin's history looks like a flat line that only takes off from 2017. The reason: in 2010 Bitcoin cost cents, and today it costs tens of thousands of dollars. On a linear scale, everything earlier disappears.

A logarithmic chart instead shows every tenfold increase at the same height: from $1 to $10 just like from $10’000 to $100’000. That makes all years comparable. How to read distances, lines and axes on it is shown in How to read the Bitcoin log chart. The chart below shows the price since 2010 with the model's three lines. Move your mouse or finger over it to see a day's values.

The price swings in waves around the trend. In bull markets it rises far above it, in bear markets it falls below. The circles mark the bear market lows: they all lie near the dashed floor line. How deep, how long and how quickly each one recovered is shown in All Bitcoin bear markets compared.

Trend, floor and top band: the three lines

The model consists of three lines. Each answers a different question.

Converted at the ECB reference rates of Nov 12, 2026 (€1 = $1.1081 = CHF 0.9232). Current values in your currency are on the Power Law page.

The trend is the middle: where the price "belongs" today given its history. Since 2010 the price was below it on about 53% of days. It was above it less often, but then often far above. Until January 2022 the trend is the Power Law line itself, 2.38 times the floor. Since then it is the middle between the floor and the top band on the log chart, today 1.62 times the floor. The reason: the highs have fallen from cycle to cycle, the lows have not. So the middle of the prices moves closer to the floor.

The floor lies at 42 % of the Power Law line. How far Bitcoin has fallen below it so far and what came next is shown in the article The Power Law floor. Measured against the line, the lowest bear market closes were 0.43 × (2011), 0.53 × (2015), 0.56 × (2018) and 0.41 × (2022). Bitcoin closed below the floor on only 3.7% of all days, most of them in 2010, 2012 and 2015.

The top band follows the cycle highs. Each high was closer to the floor than the one before: 37 × the floor (2011), 26 × (2013), 15 × (2017), 6.6 × (2021) and 2.7 × (October 2025). The top band traces this: today it is 2.63 times the floor, in November 2029 only 1.97 times. It comes down towards the floor, ever more slowly, and never reaches it. The trend stays between the two. The peaks of the cycles are getting flatter. What that means for partial sales is shown in The Bitcoin top band. Whether the four-year rhythm behind it is chance is tested in The Bitcoin four-year cycle: myth or pattern?

The five zones of the Bitcoin Power Law

Between the three lines lie five zones. The table shows how often Bitcoin has closed in each zone since July 2010.

Basis: 5’957 daily closes from Jul 18, 2010 to Nov 7, 2026 (Coin Metrics until Jan 10, 2018, OKX after that).

The boundaries lie where the past changes. One year after a day in the Floor or Accumulation zone, the price has so far been higher on 100 % of days, after a day in Fair on 78 %, after a day in Hot on only 6 %. These days come from five cycles: this is a track record, not a promise.

The zones have no fixed multiple of the trend. They follow the three lines, and those are moving together. On Nov 11, 2026, Accumulation ended at about $85’300, "Hot" began at about $138’400 and "Euphoria" at about $176’200. At the start of 2030, "Hot" begins 18% above the trend and "Euphoria" 39% above it: the model then expects a cycle high much closer to the trend than in earlier cycles.

The zones don't replace judgement. But they help you separate mood from valuation. Where the boundaries lie today in euros and francs and what followed each zone is shown in The Bitcoin valuation zones from Floor to Euphoria. When everyone is talking about new records, the zone shows you how far the price already is above its trend.

Where does Bitcoin stand in the Power Law today?

On Nov 11, 2026, Bitcoin closed at $74’019 (OKX), about €66’800 or CHF 61’700. That is 0.68 times the trend: the Accumulation zone, about 10% above the floor.

The floor rises every day. If the price stays where it is, the model has the floor reaching it around March 2027. In June 2026 Bitcoin already closed just below it once: on Jun 30, 2026, at $58’628, 0.41 times the Power Law line.

Today's figures, live in your currency:

Growth is slowing

The most important and most often overlooked point of the Power Law: the trend keeps rising, but by a smaller percentage every year. The table shows the trend on January 1 of each year.

The values from 2028 onward are not a forecast but what the model gives if the pattern continues to hold. The top band moves ever closer to the floor: at the start of 2028 it is 2.3 times the floor, in 2030 1.9 times, in 2035 1.5 times. The model itself says the big upward swings are over. The trend lies between the two, so it also grows more slowly than the floor and moves closer to it. Whether the pattern holds will be clear by December 2028. That is when the floor reaches the all-time high of October 2025 ($124’673). If Bitcoin is not above it by then, the Power Law no longer describes it.

For you this means: the Power Law no longer expects returns like those of the first ten years. It expects an asset that grows more slowly but steadily. What that means for 2030, 2035 and 2040 in euros and francs, with scenarios and the point at which the model would fail, is shown in the Bitcoin forecast based on the Power Law. What individual years could bring, you can work out in the forecast calculator.

Worked example: 10’000 euros or francs in the Power Law

The example shows the model's logic, not a promise. It only works if you hold long enough not to be forced to sell at the wrong moment. How big the cushion below your purchase price is, you can check with the floor calculator:

Where does the Power Law model come from?

The model comes from the Bitcoin community, not the financial industry. The physicist Giovanni Santostasi presented it in 2018 on the r/Bitcoin forum. In 2019 Harold Christopher Burger described the "Power Law corridor" with a lower and an upper bound, which is where the idea of the floor comes from.

Santostasi explains the power with the network: by his calculation the number of users grows roughly with the third power of time, and the value of a network rises roughly with the square of its users (Metcalfe's law). Together that gives growth roughly with the sixth power of time, close to the measured 5.7.

This reasoning is an explanation, not a proof. The model itself is purely statistical: a curve that fits past prices well.

How we calculate the Power Law on bitcoin-powerlaw.com

The Power Law line is the published formula that bitcoinpower.law and btcpowerlaw.nl also use. Its parameters are fixed, and our floor matches those sites.

The trend is our own step. Because the highs have fallen from cycle to cycle and the lows have not, the middle of the prices today lies below the line. Since January 2022 our trend is therefore the middle between the floor and the top band, and our fair value is lower than on those sites: on Nov 11, 2026, about $108’600 instead of $159’500. The floor's numbers are fixed; a day's floor never changes afterwards. The top band is refitted with every new daily close, and the trend since 2022 moves with it.

As a check, we run our own regression with every new daily close. Until the end of 2025 it confirmed the formula to within about 1%. With the weak prices of 2026 it lies about 9% lower. That is exactly why we use it only as a check: it follows the market instead of measuring it. All data, the formulas and the regression are in the methodology, the full derivation in the research paper.

What the Power Law cannot do

The Power Law is the most useful long-term model for Bitcoin we know. You should still know its limits.

• It describes the past. The formula is fitted to prices from 2010 to today. No model can prove that the pattern will continue.
• The floor is no guarantee. It was broken on 3.7% of all days, in August 2015 by 12% (0.37 times the Power Law line), most recently in June 2026.
• The trend is less certain than the floor. Since 2022 it follows from the top band, and that rests on only five cycle highs. If the next cycle runs differently, the fair value will be higher or lower than calculated today.
• The exponent depends on assumptions. A study by Baquero and Menezes (2026) shows that the exponent changes a lot if you shift the starting point of the time count. But the same study also finds that over 12 to 24 months the simple Power Law beat all the standard models tested.
• It knows no events. Bans, hacks, a breakthrough in quantum computing or an end to demand are in no formula.
• It says nothing about timing. The price can stay below the trend for years: from early 2015 to May 2017 and from June 2022 to February 2024.

Avoid any model that promises when Bitcoin will reach what price. The Power Law is more honest: it names a corridor and tells you where you stand in it. All the serious objections, tested with data, are in Criticism of the Bitcoin Power Law.

The Power Law and other Bitcoin models

The best-known model was the stock-to-flow model. It derives the price from scarcity, that is, from the ratio of existing to newly mined bitcoin. Because this ratio doubles abruptly with every halving, it expected prices after 2020 that never came. How both models have performed since 2019 is shown in the comparison Power Law vs. stock-to-flow.

The Power Law needs no halvings, only time. It expects declining growth from the start. That is why it has fit actual prices better for over 15 years. Other approaches such as moving averages are shown on the Power Law page right next to the model.

How to use the Bitcoin Power Law

1. Check the zone. Look on the Power Law page to see which zone the price is in today.
2. A plan, not a feeling. Decide what you do in which zone: for example, save regularly, buy a little more below the trend, buy nothing extra in Euphoria. If you don't hold Bitcoin alone, it helps to talk this plan through with your partner and family.
3. Run the numbers on a savings plan. How a monthly amount would have developed over the years is shown by the savings plan calculator.
4. Set a goal. How many bitcoin you need for your goal and when you reach it according to the model is worked out for you by My Goal.
5. Sort out custody. A long-term plan is only useful if your coins are safe. The basics are in the Academy, stage 2, and why coins on an exchange are not a safe place is shown by the exchange collapses from Mt. Gox to FTX.

The Power Law is not a signal for gambling. It is a compass for people who hold Bitcoin for years.