Free Bitcoin Power Law Intelligence

How the Bitcoin Power Law Chart works

This chart fits a log-log power-law regression of BTC price against days since the genesis block and ranks today’s price within the historical residual distribution. It adds probability bands, a date calculator and Years Ahead of Support.

What you enter

• Target date (today to 2040-12-31, default 2030-12-31; quick buttons 2028–2040)
• Reference BTC price (optional; blank uses the live price)

What it shows

• Historical residual percentile (0–100) with a zone label
• BTC price, fair value (midline), 5th-percentile support rail, 95th-percentile upper rail, deviation from midline, slope b and constant a
• Central 50%, 80% and 90% bands for today and the target date
• Years ahead of support, catch-up date, % above support and support multiple
• Log chart of price with the midline and both rails

How to use it

1. Read the residual percentile and its zone.
2. Compare price with fair value and the two rails.
3. Check today’s 50%, 80% and 90% bands.
4. Pick a target date to see the model range then.
5. Optionally enter a reference price for years ahead of support.

Formula

log10(price) = a + b × log10(days since 2009-01-03), least-squares fit on history since 2010 (monthly anchors before 2017, weekly closes after). Residual = log10(price ÷ fair value). Rail at percentile q = fair value × 10^(q-quantile of residuals). Percentile = share of residuals ≤ today’s. Support date: days = 10^((log10(P) − a − r5) ÷ b).

Worked example

With price $90,000, fair value $60,000 and support rail $30,000: deviation = +50%; support multiple = 3.0× (+200% above support). Years ahead is how long the 5% rail takes to reach $90,000 in model time.

How to read the result

• 90+ is labeled the resistance rail, 65–90 upper corridor, 35–65 near the midline, 10–35 lower corridor, 10 or lower near support.
• The percentile is a rank against history, not the probability of a rise or fall.
• Years ahead of support is model-time distance, not a waiting period.

Limits and cautions

• a and b are re-estimated whenever data refreshes.
• Sparse early history affects the residual percentiles.
• Date projections are model scenarios, not price targets.

Common questions

What is the Bitcoin power law model?

A regression where log10(price) is linear in log10(days since the genesis block), describing long-run growth that slows over time.

What do the rails represent?

Fair value shifted by the 5th and 95th residual percentiles, a range that held about 90% of past observations.

Is the 2030 power-law price a forecast?

No. It shows what the current fit implies if the relationship held; the model can break.