Rule of 72
Divide 72 by a growth rate to estimate how long doubling takes
- Difficulty
- Starter
- Time to result
- ~days to results
- Steps
- 4
- Confidence
- 99%
The Rule of 72 converts a percentage growth rate into an approximate doubling time. Divide 72 by the annual rate: at eight percent, the estimate is nine years. Thorp says the rule is especially accurate around eight percent; below that rate, the actual doubling time is slightly shorter than the rule predicts, while above it the actual time becomes slightly longer. The estimate can then be extended by counting doublings and recalling powers of two. At roughly 10 percent annual growth, capital doubles about every 7.2 years, producing around 14 doublings over a century. The method makes compounding tangible and also reveals the future value sacrificed by recurring consumption.
Origin
Thorp describes the Rule of 72 as well known in real estate circles and includes it in his book.
Core principles
- 01Translate annual growth into an intuitive doubling period
- 02Use the result as a first-pass estimate
- 03Expect the shortcut to be most accurate near eight percent
- 04Extend the estimate by counting repeated doublings
How to run it
- 1
Choose the rate
Express the compound growth rate as a whole annual percentage, such as eight rather than 0.08.
Watch out The shortcut assumes a stable compound rate.
- 2
Divide 72
Divide 72 by the percentage rate to estimate the number of years or periods required to double.
Pro tip At eight percent, 72 divided by eight gives nine years.
Watch out Do not present the answer as exact.
- 3
Calibrate the estimate
Remember that the rule is highly accurate near eight percent and becomes less exact farther away.
Pro tip Use it to establish scale before doing a precise calculation.
Watch out Rates below and above eight percent bend the error in different directions.
- 4
Extend through doublings
Divide a long horizon by the doubling time, then use powers of two to estimate the total multiple.
Pro tip Ten doublings are about 1,000 times and four more multiply that by roughly 16.
Watch out Nominal growth does not account for taxes, inflation, or withdrawals.
In the wild
For an investment compounding at eight percent annually, divide 72 by eight. The result is an estimated doubling time of nine years.
→ A rate becomes an intuitive time horizon without a calculator.
At 10 percent, the rule gives about 7.2 years per doubling. Over 100 years, Thorp estimates about 14 doublings, or roughly 16,000 times nominal growth.
→ Repeated doubling shows the extraordinary scale of long-run compounding.
Common mistakes
Treating the estimate as exact
The approximation's error grows as the rate moves farther from eight percent.
Ignoring real-world deductions
A nominal compound multiple does not automatically represent spendable returns after taxes, inflation, fees, or withdrawals.
Is it for you?
Best for
Quick first-pass comparisons of savings, investments, inflation, debt, or asset appreciation.
Not ideal for
Precise projections involving variable rates, cash flows, fees, taxes, or short periods.
From the transcript
“If you divide 72 by 8, you get 9. And so, the doubling time for 8% compound growth is 9 years.”
“So, it tells you something about the power of compounding and why investing for the long term really pays off.”
From the episode
#604: Master Investor Ed Thorp on How to Think for Yourself, Mental Models for the Second Half of Life, How to Be Inner-Directed, How Basic Numeracy Is a Superpower, and The Dangers of Investing Fads
Ed Thorp