Bitcoin Power Law

Bitcoin’s power-law model describes the historical relationship between its price and its age. These four views show the fitted trend, the range of historical prices around it, and where the latest price sits.

Price data through 2026-10-14. The latest daily candle may still be incomplete. Select a chart to view the full-size image.

Long-term trend

Calendar time with a logarithmic price scale makes equal percentage moves comparable across Bitcoin’s history.

Linear price view

The same observations and fitted curves on a linear price scale show the size of dollar moves.

Log–log view

Both Bitcoin’s age and price use logarithmic scales. A power-law relationship appears as a straight line.

Price relative to trend

The price-to-model ratio shows distance from the fitted trend: 1× is on the model, 0.5× is 50% below it, and 2× is 100% above it.

Methodology

The time reference is Bitcoin’s January 3, 2009 genesis date, with age measured as days since genesis plus one. The earliest 10% of post-genesis observations are excluded before fitting. The current fit uses 5,515 observations from 2011-09-08 through 2026-10-14.

Ordinary least squares fits log10(price) against log10(age): log10(P) = -16.1921 + 5.5961 log10(t). The in-sample R² is 0.9494. This measures fit to the included history, rather than predictive accuracy.

The blue curve is the power-law fit; the dotted green curve is the separately fitted median. Shading shows the 10th–90th and 25th–75th fitted quantile ranges. These describe historical price dispersion; they are not confidence intervals or guaranteed future probabilities.

Dashed curves extend the current model 365 days beyond the latest observation. The model is refitted with each refresh, so historical fitted values and deviations can change. These charts are descriptive views of the current fit, not a trading backtest.

For Bitcoin’s PAI view, see Bitcoin PAI Analysis.