How to use the Rule of 72 Calculator
- Enter the yearly return, or the inflation rate, as a percentage.
- Choose the multiple you want the money to reach.
- Read the Rule of 72 estimate for doubling and the exact figure beside it.
- Check the years to reach the multiple you chose.
Formula used
Rule of 72: years ≈ 72 ÷ rate. Exact: years = ln(multiple) ÷ ln(1 + rate). The rule is closest for rates around 6% to 10%.
Worked example
Here is the Rule of 72 Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| Return (per year) | 8 % |
| Grow money to | 3 times |
| Result | |
| Years to double (Rule of 72) | 9 |
| Years to double (exact) | 9.01 |
| Years to reach the chosen multiple | 14.27 |
Years to double at different returns
The shortcut estimate compared with the exact answer.
| Return (per year) | Years to double (Rule of 72) | Years to double (exact) |
|---|---|---|
| 2 % | 36 | 35 |
| 4 % | 18 | 17.67 |
| 6 % | 12 | 11.9 |
| 8 % | 9 | 9.01 |
| 10 % | 7.2 | 7.27 |
| 12 % | 6 | 6.12 |
How the rule works
At 8% a year, 72 ÷ 8 = 9 years to double. The exact answer, from ln(2) ÷ ln(1.08), is 9.01 years, so the shortcut is off by only a few days. At 4% the rule gives 18 years and the exact figure is 17.67; at 12% the rule gives 6 and the exact is 6.12.
The rule works because the natural logarithm of 2 is about 0.693, which would suggest 69.3, but for normal rates compounding annually makes the true constant a little higher. 72 is close to the true value for rates around 6% to 10% and divides evenly by many numbers, which makes the mental arithmetic easy.
Doubling times at common rates
At 2% money doubles in about 35 years, at 4% in 17.7, at 6% in 11.9, at 8% in 9, at 10% in 7.3 and at 12% in 6.1 years.
The table below the calculator shows the Rule of 72 and exact figures side by side. The rule is least accurate at very low and very high rates.
Other multiples
The exact formula works for any multiple. At 8%, tripling takes 14.3 years, quadrupling 18 years and growing ten times 29.9 years. Note that quadrupling takes twice as long as doubling, because it is two doublings.
A rough rule for tripling is 114 ÷ rate, and for growing ten times is 230 ÷ rate, but the exact calculation is easy here, so use it.
Inflation, debt and fees
The rule works for anything that compounds, not just investments. At 3% inflation, prices double in about 24 years, so the money in your account loses half its buying power in that time unless it earns at least 3%. A credit card at 24% interest doubles the debt in about 3 years if you pay nothing.
It also shows the effect of fees. A cost of 2% a year taken from your balance would cut its final value roughly in half over about 36 years (72 ÷ 2), which is why even small fees matter over a lifetime.
Frequently asked questions
What is the Rule of 72?
A shortcut: divide 72 by the yearly return to estimate the years needed to double money.
How accurate is it?
Very close for rates from about 4% to 12%. The calculator shows the exact figure next to the estimate.
Does it work for inflation?
Yes. At 3% inflation, prices double in about 24 years, and the value of money halves in about the same time.
Why use 72 and not 69?
69.3 is exact for continuous compounding, but 72 is closer for typical yearly compounding rates and is easier to divide in your head.
Can I use it for decreasing values?
Yes. The same idea gives the time to halve a value that falls at a steady rate, such as a falling purchasing power.
Does it include extra contributions?
No. It only applies to a single amount growing at a fixed rate. Use the investment calculator for regular deposits.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.