Rule of 72 / 70 / 69.3 Doubling Calculator
Estimate how many years it takes money to double at a given rate using the Rule of 72, 70, and 69.3, compared with the exact figure. Runs in your browser.
Years to double
| Rule | Formula | Years |
|---|---|---|
| Rule of 72 | 72 ÷ 8 | 9.0 yr |
| Rule of 70 | 70 ÷ 8 | 8.8 yr |
| Rule of 69.3 | 69.3 ÷ 8 | 8.7 yr |
| Exact (ln 2 ÷ ln(1+r)) | — | 9.0 yr |
Divide the magic number by the rate to estimate doubling time. 72 is the most popular (divisible by many numbers, accurate near 6–10%); 69.3 is the most accurate for continuous compounding (ln 2 ≈ 0.693); 70 is a simple middle ground. The exact figure uses ln 2 ÷ ln(1 + rate). All approximations are closest at moderate rates.
About this tool
The Rule of 72 is a famous mental-math shortcut: divide 72 by an annual growth rate and you get the approximate number of years for an amount to double. This tool applies that rule alongside two close cousins — the Rule of 70 and the Rule of 69.3 — and shows the exact mathematical answer for comparison. The reason there are three magic numbers is a trade-off between accuracy and convenience: 69.3 (which is 100 × ln 2) is the most accurate for continuous compounding, 72 is the most popular because it divides evenly by 2, 3, 4, 6, 8, 9, and 12 (making mental math easy) and is most accurate around 6–10% rates, and 70 is a simple middle ground often used for inflation and population growth. The exact doubling time is ln 2 ÷ ln(1 + rate). Use it to quickly gauge how powerful a return is, how fast inflation halves your purchasing power, or how long debt at a given rate takes to double. Everything runs in your browser.
How to use it
- Enter an annual growth or interest rate.
- Read the doubling time from each rule.
- Compare to the exact figure to see each rule's accuracy.
- Use 72 for quick mental math at typical investment rates.
Frequently asked questions
- What is the Rule of 72?
- A shortcut: years to double ≈ 72 ÷ annual rate (in percent). At 8%, money doubles in about 72 ÷ 8 = 9 years. It is accurate to within a fraction of a year for rates roughly between 6% and 10%.
- Why are there 72, 70, and 69.3 versions?
- They trade accuracy for convenience. The mathematically exact factor for continuous compounding is 100 × ln 2 ≈ 69.3; 70 is a rounder, slightly less precise version popular for inflation; 72 sacrifices a bit more accuracy but divides cleanly by many numbers, making mental math easy.
- Which one should I use?
- For quick investment estimates, 72 — it is easy and accurate near typical return rates. For more precision, especially at low rates or continuous compounding, use 69.3 or the exact formula. The differences are small for everyday use.
- What is the exact doubling-time formula?
- Years to double = ln(2) ÷ ln(1 + rate), where the rate is a decimal. This is exact for annual compounding; the "rules" are approximations of it that avoid logarithms.
- Can I use it for inflation or debt?
- Yes. The same rule estimates how long inflation takes to halve your purchasing power (divide the magic number by the inflation rate) or how long a debt at a given rate doubles. It applies to any constant exponential growth or decay.
- Is anything uploaded?
- No. The calculation runs entirely in your browser.