Rule of 72 Calculator
Estimate years to double at a given rate (or the rate to double in a given time), compared with the exact logarithmic answer and the approximation error.
Rule of 72 Calculator: with the default inputs, rule of 72 estimate is 9.
Interest, return or inflation rate per year.
Used when solving for the rate.
- Exact answer
- 9.01
- Approximation error
- -0.07%
- In words
- At 8% a year, money doubles in about 9 years (exactly 9.01).
- Exact time to quadruple (years)
- 18.01
Assumptions
- The exact figures assume annual compounding at a constant rate.
- The Rule of 69.3 column corresponds to continuous compounding.
| Rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact (years) | Rule of 72 error |
|---|---|---|---|---|---|
| 1% | 72 | 70 | 69.3 | 69.66 | 3.4% |
| 2% | 36 | 35 | 34.7 | 35 | 2.8% |
| 3% | 24 | 23.3 | 23.1 | 23.45 | 2.3% |
| 4% | 18 | 17.5 | 17.3 | 17.67 | 1.9% |
| 5% | 14.4 | 14 | 13.9 | 14.21 | 1.4% |
| 6% | 12 | 11.7 | 11.5 | 11.9 | 0.9% |
| 7% | 10.3 | 10 | 9.9 | 10.24 | 0.4% |
| 8% | 9 | 8.8 | 8.7 | 9.01 | -0.1% |
| 9% | 8 | 7.8 | 7.7 | 8.04 | -0.5% |
| 10% | 7.2 | 7 | 6.9 | 7.27 | -1% |
| 12% | 6 | 5.8 | 5.8 | 6.12 | -1.9% |
| 15% | 4.8 | 4.7 | 4.6 | 4.96 | -3.2% |
| 20% | 3.6 | 3.5 | 3.5 | 3.8 | -5.3% |
| 25% | 2.9 | 2.8 | 2.8 | 3.11 | -7.3% |
How this is worked out
The formula
Years to double ≈ 72 ÷ rate (%) Rate to double ≈ 72 ÷ years Exact: years = ln 2 ÷ ln(1 + r) rate = 2^(1/years) − 1 Continuous compounding: years = ln 2 ÷ r = 69.3 ÷ rate (%)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- What do you know?
- Choose one of 2 options.I know the rate — how long to double? · I know the years — what rate doubles it?
- Annual rate
- Interest, return or inflation rate per year.a percentage · from 0.01 to 500 · defaults to 8
- Years to double
- Used when solving for the rate.from 0.01 to 1000 · defaults to 9
What you get back
- Rule of 72 estimatemain answer
- Exact answer
- Approximation error
- In words
- Exact time to quadruple (years)
What this assumes
- The exact figures assume annual compounding at a constant rate.
- The Rule of 69.3 column corresponds to continuous compounding.
About this calculator
The Rule of 72 is mental arithmetic for compound growth: divide 72 by the annual percentage rate and you get the number of years for a sum to double. At 6% money doubles in about 12 years; at 9%, about 8. Because it works in both directions, it also tells you what rate you need to double in a given time — 72 ÷ 10 years ≈ 7.2%.
How to use it
Choose whether you know the rate or the time, enter it, and compare the estimate with the exact answer computed from logarithms. The table underneath shows doubling times at common rates alongside the Rule of 70 and Rule of 69.3, so you can see where each shortcut is closest.
Why 72, and how wrong is it?
The exact doubling time is ln 2 ÷ ln(1 + r). For continuous compounding that's 0.693 ÷ r, which gives the "Rule of 69.3". Annual compounding makes the true time a little longer, and 72 happens to fit best near 8% — it's also divisible by 2, 3, 4, 6, 8, 9 and 12, which is why it stuck. The error is under 2% between about 5% and 12%. At 2% the rule says 36 years versus an exact 35; at 20% it says 3.6 versus 3.8. Use 70 for low rates and 76 for very high ones if you want more precision in your head.
Where it's useful
- Investing: at a 7% real return, purchasing power doubles about every ten years — so a 25-year-old's dollar is roughly 16 dollars by 65.
- Inflation: at 3%, prices double in 24 years; a fixed pension loses half its buying power over a retirement.
- Debt: a credit card at 24% doubles the balance in three years if you pay nothing.
- Fees: an extra 1% a year in costs over 36 years means you end up with half of what you'd otherwise have.
Beyond doubling
To triple, use 114 ÷ rate; to quadruple, just double the doubling time (shown in the results). And remember the rule assumes a steady rate — real returns vary, which slightly lengthens actual doubling times compared with the average rate.
Frequently asked questions
▸What is the Rule of 72?
A quick estimate of doubling time under compound growth: years ≈ 72 ÷ annual rate in percent. At 6% that's 12 years.
▸How accurate is the Rule of 72?
Within about 2% of the exact answer for rates between roughly 5% and 12%. It overstates doubling time at low rates and understates it at high ones.
▸Rule of 72 vs Rule of 70 vs Rule of 69.3 — which should I use?
69.3 is exact for continuous compounding, 70 is close for low rates and easy to divide, 72 is best for typical investment returns around 6–10% and has more divisors. Any of them beats not estimating.
▸How long does money take to triple?
Roughly 114 ÷ rate. At 8% that's about 14 years, versus 9 years to double.
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