Rule of 72 Calculator
How long money takes to double, triple or quadruple by the rule of 72 and exactly, with the error between them, and the rate needed for a given time.
Result
Exact years: 11.8957 years
Assumes the rate compounds once a year and stays the same throughout.
- By the rule
- 12
- Rule minus exact, years
- 0.1043
- Error as a share of the exact answer
- 0.88%
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Results are arithmetic on the returns, rates and horizons you enter, not a forecast and not investment, tax or retirement advice. The site supplies no expected return, inflation rate, contribution limit, tax rate or withdrawal rate. Real returns vary from year to year, and fees, taxes and the order of returns all change the outcome. Check anything that matters with a qualified adviser. Read the full disclaimer
How to use the Rule of 72 Calculator
- Enter an annual rate of return or interest.
- Choose whether you want the time to double, triple or quadruple.
- Read the rule's quick answer beside the exact one, and optionally enter a number of years to see the rate that target needs.
The rule and the exact answer
Money growing at a rate r a year doubles when (1 + r)^n = 2, so the exact number of years is n = ln 2 ÷ ln(1 + r). The rule of 72 replaces that with 72 ÷ the rate in percent, which anyone can do in their head. The page shows both, and the error between them, because the error is the interesting part: the rule is almost exactly right at 8% and drifts in both directions from there.
Tripling and quadrupling
The same reasoning with ln 3 and ln 4 gives the rule of 114 for tripling and the rule of 144 for quadrupling. Quadrupling is doubling twice, so the rule of 144 is the rule of 72 applied twice. At 6%, the rule of 114 says 19 years to triple against an exact 18.8542.
The rate for a given time
Turned around, the rule says the rate needed to double in n years is 72 ÷ n percent. Exactly, it is 2^(1/n) − 1. That exact rate is also the compound annual growth rate of a doubling over n years, which the CAGR calculator gives for any start and end.
With your numbers
- By the rule: 72 ÷ 6 = 12 years
- Exactly: ln 2 ÷ ln(1 + 6%) = 11.8957 years
Quick reference
Assumes the rate compounds once a year and stays the same throughout.
| Example | Exact years |
|---|---|
| Doubling at 6% | 11.8957 |
| Doubling at 8% | 9.0065 |
| Doubling at 2% | 35.0028 |
| Doubling at 20% | 3.8018 |
| Doubling at 10% | 7.2725 |
| Tripling at 6% | 18.8542 |
| Rate to double in 10 years | 10.2448 |
Common questions about the Rule of 72 Calculator
- How accurate is the rule of 72?
- Very, near 8%, and less so further away. At 8% it gives 9 years against an exact 9.0065. At 2% it says 36 against 35.0028, and at 20% it says 3.6 against 3.8018. For the rates most savers see, it is within a few months.
- Why 72 and not 69.3?
- The exact doubling time is ln 2 ÷ ln(1 + r), and for small rates that is close to 69.3 ÷ the rate in percent. 72 is used because it fits typical rates better, since ln(1 + r) is a little less than r, and because it divides evenly by 2, 3, 4, 6, 8, 9 and 12.
- What rate do I need to double my money in 10 years?
- By the rule, 72 ÷ 10 = 7.2%. Exactly, 2^(1/10) − 1 = 7.1773%. Enter the years in the optional field to see both for any target.
- Does it work for inflation?
- Yes, the arithmetic is the same: at 3% inflation, prices double in about 24 years by the rule, 23.4 exactly. It works for anything growing at a steady rate.