Orange Law

Power Law

Bitcoin is not a corporation racing toward saturation and death; it is a city spreading like an epidemic, where users cube with time, value squares with users, and price is simply the network's age raised to the sixth power.

BitcoinUSD

$77,903+0.62%−49.8% vs fair

−0.99σbelow fair value

2.02× the floor

−2σ−1σFair+1σ+2σ

Floor

$38,606

Fair

$155,116

Top

$623,240

Scale-invariant pathR² 0.962

Scroll or pinch to zoom. Drag to pan. Double-tap clears A-B.

$0.010$0.10$1$10$100$1,000$10,000$100,000$1.0M2012201420162018202020222024202820322036FLOOR−1σFAIR+1σTOPlog–log · days since GenesistodayPOWER LAWFLOOR

Selected span

Pick two dates, or tap the chart. Future dates use the model path.

Enter two dates to measure a span.

Bands are log-normal quantiles around the fitted law (σ = 0.302 dex). Cycle swings of about ±1σ are typical; a print more than 3σ below the fit would falsify the floor.

Your buys

Upload your buy dates + dollar amounts to plot your stack.

The network

Zoom out. Trust the curve.

Users cube with time. Price grows with those users. Same slope through every boom and crash — the curve doesn’t care.

Sound off

Your stack

What is it worth later?

Enter how many bitcoin you own and a date. Each quantile is the model price that day, the matching stack value, and the annualized return versus today.

BTC

1 BTC on Nov 1, 2031·1,826 days · 5.00 years

$633,207

Fair-value stack·1 BTC × $633,207

+712.8% total

+52.1% / yr

Today $77,903

Floor

$157,596 / BTC

$157,596

+102.3% tot·+15.1% / yr

−1σ

$315,897 / BTC

$315,897

+305.5% tot·+32.3% / yr

Fair

$633,207 / BTC

$633,207

+712.8% tot·+52.1% / yr

+1σ

$1.27M / BTC

$1.27M

+1,529% tot·+74.8% / yr

Top

$2.54M / BTC

$2.54M

+3,166% tot·+100.8% / yr

Self-custody

Hold the keys

The power law only helps if you still hold the coins. A hardware wallet keeps the keys offline — Trezor built the first one, and it still only signs what you confirm on the screen.

  • Keys stay on the device, not on an exchange.
  • Open-source firmware you can verify.
  • Ships from Trezor — not a reseller.
Get a Trezor

Affiliate link — Orange Law may earn a commission if you buy. Same price to you.

Model forwards

5-year path

Nov 1, 2031

  • Floor$157,596+102.3%+15.1% /yr
  • −1σ$315,897+305.5%+32.3% /yr
  • Fair$633,207+712.8%+52.1% /yr
  • +1σ$1.27M+1,529%+74.8% /yr
  • Top$2.54M+3,166%+100.8% /yr

200-week moving average

How Cheap is Bitcoin Today?

Bitcoin’s 200-week moving average (200WMA) is the average of weekly closing prices over nearly four years and functions as a slowly rising long-term cost basis and historical cycle floor. When the market price trades near or below that line, Bitcoin has historically been considered cheap and in an accumulation zone at cycle bottoms; when price trades at large multiples above the 200WMA, it has typically been regarded as expensive and late-cycle. Today is 1.19× — closes below the 200WMA occur 8.3% of days.

All days with a 200-week average · May 11, 2014 – Sep 22, 2026 · 4,518 days · Current multiple 1.19×

  • Below 1.0×
  • 1.0–1.2×
  • 1.2–2.0×
  • 2.0–4.0×
  • ≥4.0×

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3–4

4–5

5–6

≥6

Bitcoin price ÷ 200-week moving average

Source: daily USD close. 200WMA = 200-period SMA of weekly Sunday closes, forward-filled to each day. Not investment advice.

Scale-free nature

More Power Laws in Nature

Same log-log plane as Bitcoin. Each line is y = A xβ with the exponent from the source paper — slope is the law. Zipf, city rank-size, and Bitcoin’s on-chain wealth tail sit near β = −1. Kleiber rises; Pareto and Gutenberg–Richter decay at other slopes.

10⁻⁹10⁻⁷10⁻⁵10⁻³10⁻¹10¹110¹10²10³10⁴10⁵10⁶relative y (native units, log)relative scale x (log)Earthquake Size & Frequency(Richter)City Population Sizes(Auerbach-Zipf law)Word Use Frequencies(Zipf's law)Bitcoin Wallet Balances(on-chain Pareto)Income & Wealth(Pareto's law)

  • Income & Wealth (Pareto's law)

    Pareto, Cours d’économie politique (1896–97)

  • Word Use Frequencies (Zipf's law)

    Zipf, Human Behavior and the Principle of Least Effort (1949)

  • Earthquake Size & Frequency (Richter)

    Gutenberg & Richter 1944; Kanamori 1977 (E ∝ 10^{1.5 M})

  • City Population Sizes (Auerbach-Zipf law)

    Auerbach 1913; Zipf 1949; Gabaix, AER 1999

  • Animal Metabolic Rates (Kleiber's Law)

    Kleiber 1932; West, Brown & Enquist, Science 1997

  • Bitcoin Wallet Balances (on-chain Pareto)

    Kondor et al., PLOS ONE 2014 (power-law tail); Santostasi & Perrenod on-chain α ≈ 1.07; rank-size slope ≈ −1 (Santostasi 2025)

The $1 trillion club

What is the Fastest Horse In the Race?

Clock starts at founding — Genesis for Bitcoin. Bitcoin is daily price times circulating supply. The others are quarterly market cap from the IPO through the first $1 trillion print. Bitcoin is the orange used above.

$1M$10M$100M$1B$10B$100B$1T051015202530354045USD market cap (log)years since founding / Genesis$1 trillionBitcoin12 yearsMeta17.4 yearsTesla18.3 yearsGoogle21.4 yearsAmazon24.2 yearsNVIDIA30.1 yearsApple42.3 yearsMicrosoft44.1 years
  • Bitcoin12 years
  • Meta17.4 years
  • Tesla18.3 years
  • Google21.4 years
  • Amazon24.2 years
  • NVIDIA30.1 years
  • Apple42.3 years
  • Microsoft44.1 years

Equities

Stocks or Bitcoin?

The power law is a diminishing-return curve: the same exponent on a larger age each year, so the implied one-year gain shrinks. Today that path still prices a 36.7% year. On a phone the orange line is only that smoothed curve, so it stays readable. The S&P line is still the actual trailing return through today, then 10% dashed. Drag either chart. Tap a name to isolate the line.

Power-law 1 year

36.7%

implied, today

S&P 500, 1 year

18.6%

actual trailing total return

Meets 10%

2068

2068-03-17

$1 since 2010

1.1 million×

S&P 9.6×

One-year return

Solid lines are trailing one-year returns through today. The faint orange line is the smoothed power-law one-year return, also through today. Dashed bitcoin continues that power law. Dashed S&P is a 10% assumption.

-50%0%10%100%1,000%10k%20102015202020252030204020502060annualized returnyearTodayMeets 10% 2068Power Law 1 YearCAD Parity (2028)Gold Parity (2035)Bond Parity (2043)

Power Law 1 Year, through today

2026-09-22-23.5%—

Solid is actual history. The faint line is the power-law one-year return through today. Dashed is projected.

CAD Parity (2028)$5.2T

Gold Parity (2035)$31T

Bond Parity (2043)$145T

Growth of $1 (log)

$1 in bitcoin versus $1 in the S&P 500 total-return index from July 2010. Dividends stay in.

1×10×100×1k×10k×100k×1M×20102013201520172019202120232025multiple of starting $1 (log)year9.6×1.1 million×

2026-09-221.1 million×9.6×

The law

P(t) ∼ tβ

Santostasi and Perrenod show the exponent is not a free fit. Address growth scales as t3.05 (epidemic spread on a scale-free network) and price scales as N1.84 (generalised Metcalfe). Their product is the observed β.

β
5.69
σ
0.302 dex
R²
0.961

Fit on daily closes from 17 July 2010 (day 560 after Genesis) through February 2026. Floor is the −2σ quantile; a year below −3σ is the published falsification test. Fiat units other than USD (CAD, EUR, TRY, and the rest) convert each day’s dollar close by that day’s FX — the path moves with the currency, it is not a frozen multiplier. GOLD is not a dollar conversion: it is Giovanni’s Gold/BTC power law (β = 5.41, σ = 0.330 dex) in ounces per bitcoin, using each day’s gold price. Native CAD, gold, and live FX still feed the day-over-day change. Compare overlays use Yahoo Finance adjusted closes (S&P 500 total return, XIC.TO for the TSX, CNQ.TO, NVDA, AAPL, COST) converted into the selected unit the same way bitcoin is, then indexed to bitcoin's price at the left edge of the view so each line is the growth of the same starting dollar.

Model by Giovanni Santostasi · @Giovann35084111. Paper with Stephen Perrenod: A Mechanistic Derivation of the Bitcoin Price Power Law.

Independent educational chart — not affiliated with Giovanni. Questions: hymerschmidt@hotmail.com · About · Privacy.