Bitcoin power law: trend price and chart

The line on any date

Pick a date, past or future, to see where the fitted line and its corridor sit. A date after today shows where the line runs if the past pattern held, which it may not.

The fit

Data

5927 daily closes, August 18, 2010 to November 8, 2026

Formula

log10(price) = -16.185 + 5.595 × log10(days since 3 January 2009)

Share of variance explained (R²)

96.0%

Corridor, 5th to 95th percentile

0.44× to 3.6× the trend price

Where the line sits on 1 January

The fitted line and its corridor on the first day of each coming year, in US dollars. These are points on a curve fitted to the past, not price targets.

How it works

Every daily close since 18 August 2010 becomes a point: x is log10 of the number of days since the genesis block of 3 January 2009, and y is log10 of the price in US dollars. An ordinary least squares line through those points gives the intercept a and the exponent b, so the trend price on day d is 10^a × d^b. The corridor is the range that held 90% of past closes: the 5th and 95th percentiles of their distance from the line. The fit is recalculated every time the price history is updated.

What the model cannot tell you

A power law describes the past, and part of its good fit comes from how far bitcoin's early price moved. The exponent depends on the window: it is 5.59 fitted to every close, but 5.24 fitted from 2013 on. Prices have spent years far above and far below the line, and nothing guarantees the pattern continues. Use it to put today's price in context, not to plan around a target.