The formula

P(d) = 10a · db, where P is the trend price in US dollars and d the number of days since the genesis block on 3 January 2009.

TermValueMeaning
a−17.0908Intercept on the log-log chart
b5.82985Exponent: the slope of the line on the log-log chart
R²0.958Share of the variation in log prices explained by the line

Taking logarithms turns the curve into a straight line: log10(P) = a + b · log10(d). That is why the model looks straight on a log-log chart and curved on a normal time axis.

What the exponent means

Each time the network's age doubles, the trend value rises by a factor of 2b — with b ≈ 5.83 that is about 57 times. Because doubling the age takes longer and longer, the yearly growth rate of the trend falls over time.

Worked examples

  • 1 January 2030 is day 7,668: 10−17.0908 · 7,6685.82985 = $360,010.
  • 1 January 2035 is day 9,494: the same calculation gives $1,250,640.

How the line is fitted

The parameters come from a median regression (quantile regression with q = 0.5) of log10(price) on log10(days) over every daily close from 18 July 2010 to 14 October 2026 — 5,933 observations. The bands around the line are percentiles of the residuals since 1 January 2015. With every new day, a and b shift slightly; the live model shows the current fit and a backtest of earlier fits.

Limits

A good fit to the past is not proof of a law of nature. The model has one input — time — and contains no information about supply, demand, regulation or competition. It is a description of a pattern, useful for scale and orientation, not a prediction for a specific date.

Note: Model values, not a forecast and not investment advice. The model describes the corridor Bitcoin has traded in; it does not predict any single day.

Open the live model →

More guides

This site and its domains are part of the Bitcoin Asset Group portfolio. Make an offer