Experimental price model

Bitcoin power-law model

Explore a long-term curve fitted to CoinGecko BTC/USD daily closes with log-log regression and its historical residual range.

Log-log regression

Historical trend and assumption-based future range

Compare actual closes with the central power-law curve. The future dashed line assumes the same coefficients continue; it is not a price forecast or target.

Loading model data
The future dashed line is not a forecast or target.

This range extends the historical curve by assuming the same mathematical relationship continues. It does not guarantee a future price range.

Latest snapshot close
$84,417
2026-09-26
Central curve on that date
$116,009
2026-09-26
Difference from central curve
−27.2%
actual close ÷ central curve − 1
Log-space R²
0.9130
not a forecast probability
Actual CoinGecko closesCentral power-law curveHistorical log-residual 5th–95th boundaries
Loading chart data.
Model coefficients and input range
α
-33.791347
β
5.179387
Input range
2013-04-28–2026-09-26
Time origin
2009-01-03
Conditional model values at year end
Reference dateCentral power-law curve5th-percentile boundary95th-percentile boundary
$216,205$84,139$660,341
$278,346$108,322$850,132
$354,160$137,826$1,081,685
$445,824$173,498$1,361,649
$556,071$216,402$1,698,370

Downloaded data snapshot · not a live price · not investment advice or a trading signal

A straight-line regression follows the log transform

For each date, t is the number of UTC days since January 3, 2009. The model fits ln(P) = α + β × ln(t) to CoinGecko close P by ordinary least squares, then converts the central curve back with exp(α + β × ln(t)).

Coefficients are not copied from an external model. They are recalculated from the complete daily-close snapshot published by BtcCal. Updating the CSV can therefore change both coefficients and future extension values.

Boundary lines show historical residuals

The model measures the log difference between each actual close and the central curve, then uses the 5th and 95th percentiles as boundaries. These lines describe the spread of past observations; they are not statistical confidence intervals, support or resistance levels, or a future price range.

Log residual = ln(actual close ÷ central curve)

Historical fit does not establish predictive power

A relatively smooth relationship between Bitcoin price and time in log space does not guarantee that the same coefficients will continue. Price also responds to demand, liquidity, regulation, macroeconomic conditions, and market structure.

Daily prices are not independent experiments, so the R² shown here must not be read as a probability of future accuracy. The dashed extension through 2032 is a conditional calculation for inspecting the model's shape.

Read the data range and source with the model

Inputs are downloaded CoinGecko BTC/USD UTC daily closes. A visitor's browser does not call CoinGecko or a live-price API.

Read the price-data details →