Bitcoin Power Law Model: Live Chart, Calculator & Formula

Calculators

Day by day for any date from 2010 to 2060. The selected day is marked in the chart. All amounts in US dollars, because the model is fitted on dollar prices.

Date (past or future)

Tip: click the chart to pick a day. Inside the chart, arrow keys move by day, Shift + arrow by month.

Model calculation, not a forecast or investment advice.

Model values year by year

Values on 1 January of each year. For past years the actual daily close is shown alongside.

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

The formula

P(d) = 10^a · d^b

Ptrend price in US dollars ddays since the genesis block (3 January 2009), today 6,493 a−17.091 (intercept, 10^a ≈ 0.811 · 10⁻¹⁷) b5.830 (exponent, the slope on the log-log chart) R²0.958 (share of the variation in log prices explained by the line)

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 came close to the floor 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 April 13, 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 four 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 January 09, 2034. The floor would only get there on March 18, 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.

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

What does the power law model say today?

On October 14, 2026 the trend stands at $136,516, the floor at $67,824 and the ceiling at $644,592. The price of $81,576 sits at 11 out of 100 in the corridor.

What does the model say for 2030?

On 1 January 2030 the trend is at $360,010, the floor at $178,860 and the ceiling at $1,699,863. These are values of the extended lines, not a forecast of the actual price.

When does Bitcoin reach one million dollars according to the model?

The trend line reaches one million dollars on January 09, 2034, the floor on March 18, 2037. Use the “Target price” calculator for any other amount.

Where is the floor of the Bitcoin price?

The model floor is $67,824 today, which is ×0.50 of the trend. It rises with the trend line every day. Since 2015 the price was below it on 1% of all days, so it is a historically rare boundary rather than a hard floor.

Why does the model count days since the genesis block?

3 January 2009 is the start of the network and therefore the natural zero point. With a different starting point the exponent and the curvature of the line change. The genesis block is the usual, but chosen, zero point.

Why do other sites show different values?

The parameters depend on data source, period and method. This page uses a median regression on every daily price since July 2010, which reacts less to bubbles than the usual least-squares method. Other sites use fixed published parameters or other periods, so their lines sit somewhat higher or lower.

How current is the data?

The price updates every minute (Kraken, with CoinGecko as fallback). Missing daily closes since the last data update are added on load. The model parameters are re-estimated whenever the dataset is updated, most recently with data to October 14, 2026.

Is this a price forecast or investment advice?

No. The model describes a statistical relationship in past data. It is not a forecast, not a recommendation and not investment advice.

May I use the values?

The model values yes, with a source credit and the data date. Historical prices come from Coin Metrics (Community Data, CC BY-NC 4.0) and Kraken, and their terms apply.

Method and data

Price data: Coin Metrics Community Data (USD reference rate) from 18 July 2010, extended with daily closes from Kraken (XBT/USD). 5,933 days in total, without gaps up to October 14, 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: Kraken (XBT/USD), with CoinGecko as fallback (Powered by CoinGecko), fetched through this site's own server. Euro conversion via Kraken's XBT/EUR to XBT/USD ratio.

Not investment advice. All content is for information and education. It is not a solicitation to buy or sell bitcoin or any other asset. Crypto assets are highly volatile and a total loss is possible. Past performance is not a reliable indicator of future results.

The Bitcoin Power Law Model.