The Bitcoin Power Law Model.

In plain words: why does the model expect such high prices?

At its core the model does one thing: it takes every Bitcoin price since 2010, draws a line through them and extends that line into the future. The line shows how fast the price has risen on average so far, through every high and every crash. The large numbers for the future come about in four steps:

1. So far the rise has been very steep. At the start of 2015 one bitcoin cost about $310, at the start of 2020 about $7,200, on 14 October 2026 $81,576. The line captures exactly this rise.
2. The rule behind the line is simple. Each time Bitcoin becomes twice as old, the trend value rises to about 57 times its level. Bitcoin is about 18 years old today. At twice that age, in 2044, the trend would stand at about $7,800,000 under this rule.
3. Growth slows down, but it does not stop. Today the trend rises by about 38% a year, by about 25% in 2035 and still about 15% in 2050. Even smaller rates add up to very large amounts over decades, much like compound interest. That is how the trend reaches about $3,500,000 per bitcoin in 2040 and about $18,000,000 in 2050.
4. The usual explanation. Supporters explain the pattern with the network effect: the more people use Bitcoin, the more useful it becomes, which attracts further users. At the same time the supply is capped at 21 million bitcoin. Growing demand meets a fixed supply.

An assumption, not a promise. The model only knows the past, and no law forces the price to follow the line. For scale: at $18,000,000 per bitcoin, all 21 million bitcoin together would be worth about $374 trillion, many times the value of all the gold in the world. Whether Bitcoin will ever be worth that much is open. That is why the calculators always show the cautious floor path and the result without any price rise as well.

What is the Bitcoin power law?

The Bitcoin power law describes Bitcoin's long-term price as a function of the time since the network started. Plot the price and the number of days since the genesis block of 3 January 2009 on two logarithmic axes, and more than 15 years of daily prices sit close to a straight line. A straight line on a log-log chart is the signature of a power law.

The price swings widely around that line. In euphoric phases it traded at several times the trend, in bear markets well below it. So the model says nothing about tomorrow's price. It shows the corridor the price has moved in for many years, and where that corridor runs in the future if the pattern continues.

Today, 14 October 2026, the trend stands at $136,516. The price of $81,576 deviates from it by −40.2%.

The formula

Take logarithms and the curve becomes a line: log₁₀(P) = a + b · log₁₀(d). The exponent b sets how fast the trend grows. Each time the network's age doubles, the trend value rises by a factor of 2^b; with b ≈ 5.8 that is roughly 57 times.

Why growth slows over time

Every additional year is a smaller step for an older network. That is why the trend grows more slowly in percentage terms even though it stays a straight line on the log-log chart. Today the trend line rises by +38% a year; by 2030 the rate will be lower. On a time axis this shows as a curve that flattens to the right.

Worked example

On 1 January 2030 Bitcoin is 7,668 days old. Plugged in, 10^a · 7,668^b gives a trend value of $360,010. The calculator above runs exactly this calculation for any day.

Floor, bands and ceiling

Besides the trend line, the chart shows four parallel lines. They come from the distribution of daily deviations from the trend since 1 January 2015:

• Floor (1st percentile, ×0.50 of trend, today $67,824): the price was below it on only 1% of all days since 2015. It dipped briefly below it in late summer 2015, around the turn of 2022/23 and in summer 2026.
• Lower band (10th percentile, ×0.59): the price was below it on only 10% of days since 2015.
• Upper band (90th percentile, ×2.43): the price was above it on 10% of days since 2015, almost only in cycle highs.
• Ceiling (99th percentile, ×4.72, today $644,592): since 2015 the price reached this level only around the turn of 2017/18 (December 2017 to mid-January 2018).

Why start in 2015? In the early years the market was tiny and the price at times traded more than 20 times above the trend, 23 times in June 2011. Including those years would make today's bands unrealistically wide. The trend line itself is fitted on every day since July 2010.

Corridor position and zones

The corridor position from 0 to 100 tells you on what share of all days since 2015 the price, relative to trend, was lower than on the day you look at. Today it reads 11. The zones follow from it: below 1 “below floor”, 1–10 “low in corridor”, 10–35 “below trend”, 35–65 “near trend”, 65–90 “above trend”, 90–99 “high in corridor”, above 99 “above ceiling”. The names only describe position; they are not a valuation or a signal.

Time shift

The time shift turns the deviation into time: on which day was the trend line where the price stands today? Right now the price equals the trend of 13 April 2025. A negative value means the price lags behind the trend.

Reading the chart

• Log axis (default): the x axis is logarithmic in days since genesis and labelled with years. Only this way does the trend appear as a straight line. Years move closer together towards the right.
• Time axis: linear time, as in a regular price chart. The trend becomes a curve that flattens to the right.
• Linear price axis: dollar amounts at equal spacing. Early years vanish at the zero line and the size of future values becomes tangible.
• Dashed lines to the right of today extend the model lines.
• Oscillator below the chart: the deviation from trend as a multiple, ×1 meaning exactly on trend. It lets you compare cycles across all price levels.
• H 2012 to H 2024: the halvings, when the block reward is cut in half. The next one is expected around April 2028 (block 1,050,000); the exact day depends on block times.
• Backtest: overlays the trend line you would have fitted with data up to the chosen year-end only. The dot marks the end of the data known at the time.

Controls: drag to pan. Zoom with the magnifier buttons, Ctrl + mouse wheel or two fingers; double-click resets. A click selects the day for the calculator.

The six calculators

Date

For any day between 2010 and 2060. For past days it shows the actual daily close, the deviation from trend, the corridor position and the zone. For future days it shows the trend, bands, floor and ceiling, plus the annual return needed to get from today's price to the trend value on that day.

Target price

Turns the formula around and asks for the date: when does the trend reach a given price? For one million dollars the current line says 9 January 2034. The floor would only get there on 18 March 2037.

One-off buy

What would an amount invested on a given day be worth today? With the bitcoin amount, today's value, the multiple and the annual return, plus the value if the price sat exactly on the trend on a target date.

Savings plan

Monthly instalments at the daily close on the same calendar day. Result: amount invested, bitcoin stacked, average price and value. If the end lies in the future, later instalments and the final value use the trend value.

Withdrawal

How long do bitcoin holdings last if a fixed amount is withdrawn every month? The calculator sells as much bitcoin each month as the withdrawal needs and can raise it every year. It runs four price paths side by side: price stays at today's level, price at the floor, price keeps today's position relative to trend, price on the trend. A start date in the past uses actual prices up to today. Taxes and fees are not included.

BTC needed

The withdrawal calculator in reverse: how much bitcoin do you need to withdraw a fixed amount every month for a chosen number of years, optionally rising each year? Each month counts how much bitcoin the withdrawal costs at that month's price. The calculator shows this for the same four price paths, plus today's value. The floor path is the most cautious assumption. In detail, with examples.

Euro and sharing

Chart, key figures, table and calculators can be switched to euros. Past values are converted at the ECB reference rate of each day, future values at today's rate. The model itself stays fitted on dollar prices, so in euros the trend line is not perfectly straight. "Share result" creates a link that reopens the calculator with the same inputs and currency.

Where does the model come from?

Power laws show up in many fields, for example in city sizes, the energy of earthquakes or the connectivity of large networks. There they mostly describe distributions; in the Bitcoin model it is growth over time. First observations circulated in forums from around 2014, and the relationship became widely known from 2019. It was popularised mainly by physicist Giovanni Santostasi and by Harold Christopher Burger, whose widely read article of January 2019 described a long-term power-law growth corridor.

A common explanation links the model to network effects: if the number of users itself grows by a power law and a network's value rises faster than its user count, the price again follows a power law. That mechanism is not proven. Published parameters differ because they were estimated with different data, periods and methods. The exponent is usually around 5.8 to 6.

How stable is the model?

A good test: what would the model have given with less data? The table shows which exponent you would have estimated with data up to each year-end, and which trend value that line gives for today. In the chart, any of these lines can be overlaid via “Backtest”.

In the early years the exponent moved a lot: above 7 in 2014, 5.5 in 2016. Since 2019 the estimates sit closer together, between 5.8 and 6.1. That suggests some stability. Still, for 2040 even the fits since 2019 differ by up to 1.8 times, and the 2013 and 2014 fits by more than ten times.

Limits and criticism

• Curve fitting, not a law of nature. The line describes the past. It does not follow that it will keep holding.
• Statistical pitfalls. Strongly trending time series easily produce a high R² even without a real relationship. Deviations are also autocorrelated over months, so the R² overstates the evidence and is not proof.
• Log scales deceive. A gap that looks small on the chart can mean tens of thousands of dollars. The linear axis makes that visible.
• The corridor can break. Regulation, technical failures, new market structures or macroeconomic shocks are not part of the model.
• Time is the only input. Supply, halvings, demand and interest rates play no part.
• Dollar basis. The model is fitted on US dollar prices. In euros, exchange rates produce a slightly different line.

Frequently asked questions

Method and data

• Price data: Coin Metrics Community Data (USD reference rate) from 18 July 2010, extended with daily closes from a crypto exchange (BTC/USD). 5,933 days in total, without gaps up to 14 October 2026. Days end at 00:00 UTC.
• Trend: median regression (quantile regression with q = 0.5) of log₁₀(price) on log₁₀(days since genesis) across all days.
• Bands: 1st, 10th, 90th and 99th percentile of deviations from trend since 1 January 2015, as constant offsets in log space.
• Backtest: the same regression, each time using only data up to 31 December of the year.
• Live price: exchange price BTC/USD, fetched through this site's own server. Today's euro rate via the BTC/EUR to BTC/USD ratio on the same exchange.
• Euro view: ECB EUR/USD reference rates (source: European Central Bank), last published rate on weekends and holidays; days after the data cut-off and projections at today's rate.