Rule of 72 Calculator
Estimate how long it takes an investment to double using the Rule of 72 (years ≈ 72 / rate%), and see the exact logarithmic answer beside it. Compares the Rule of 72, 70 and 69.3 approximations, shows each rule's error, supports any compounding frequency, and works in reverse to find the rate needed to double in a target number of years.
Input
The nominal annual rate of return.
Used for the exact (logarithmic) value; the shortcut rules don't depend on it.
Output
| Method | Result | Error vs exact | Best for |
|---|---|---|---|
| No data yet | |||
Guides
The Rule of 72 is a mental-math shortcut for estimating how long an investment takes to double at a fixed compound growth rate. Divide 72 by the annual interest rate (as a whole-number percent) and you get the approximate number of years to double: at 8% a year, money doubles in roughly 72 / 8 = 9 years. This calculator runs that shortcut in both directions and — crucially — puts the exact answer right beside it, so you can see exactly how far the approximation strays.
How to use it
- Pick a direction. Rate → years to double takes an interest rate and estimates the doubling time. Years to double → required rate reverses it: give a target number of years and get the rate you'd need.
- Enter the rate or the years.
- Optionally choose a compounding frequency (annual, monthly, continuous, and so on). This only affects the exact logarithmic value — the shortcut rules ignore it.
The result shows the headline Rule-of-72 estimate, the exact value, and a comparison table listing the Rule of 72, the Rule of 70, the Rule of 69.3, and the exact figure, each with its error against the exact answer. Everything is computed in your browser; nothing is sent to a server.
Why it works, and where it breaks
Doubling under compound interest is really a logarithm problem. The exact doubling time for an annually compounded rate r is ln(2) / ln(1 + r/100), and the exact rate to double in t years is (2^(1/t) − 1) × 100. Because ln(2) ≈ 0.6931, the "true" constant for continuous compounding is about 69.3, not 72. So why 72? Because 72 has many small divisors (2, 3, 4, 6, 8, 9, 12…), making the mental division easy, and it happens to compensate nicely for the gap between continuous and once-a-year compounding in the range people care about most.
The rule is most accurate for rates around 6–10%, where its error is well under 1%. Away from that band the drift grows: at very low rates (1–2%) the Rule of 70 or 69.3 is closer, while at high rates (20%+) all three shortcuts overstate the time. The calculator's error column makes this visible at a glance.
Rule of 72 vs 70 vs 69.3
They're the same shortcut with a different numerator. 69.3 (≈ 100·ln 2) is the mathematically exact constant for continuous compounding and is the most accurate at low rates. 70 is a common compromise that's easy to divide. 72 is the most popular precisely because of its divisibility, and it's the best fit for typical mid-single-digit to low-double-digit returns.
Does it only apply to money?
No. Any quantity growing at a constant percentage rate doubles on the same schedule — population, inflation eroding purchasing power, bacterial growth, or website traffic. Plug the growth rate in as the "interest rate" and the doubling time follows.
The figures here are estimates for general education, not financial advice.