Rule of 72 Calculator: How to Calculate Doubling Time
Estimate how many years it takes for money to double at a constant annual compound rate using the Rule of 72.
How to calculate the Rule of 72: years to double ≈ 72 ÷ annual rate (%). At 8%, money roughly doubles in 72 ÷ 8 = 9 years. The exact answer is ln(2) ÷ ln(1 + r).
| Annual rate | Rule of 72 | Exact |
|---|---|---|
| 1% | 72.0 | 69.7 |
| 2% | 36.0 | 35.0 |
| 3% | 24.0 | 23.4 |
| 4% | 18.0 | 17.7 |
| 5% | 14.4 | 14.2 |
| 6% | 12.0 | 11.9 |
| 7% | 10.3 | 10.2 |
| 8% | 9.0 | 9.0 |
| 9% | 8.0 | 8.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
| 15% | 4.8 | 5.0 |
| 20% | 3.6 | 3.8 |
Full table from 1% to 20%, with Rule of 70 and 69.3 → · Compound interest calculator · How compound interest works
Rule of 72 table: years to double at 1%–12%
Divide 72 by the rate to estimate doubling time. "Exact" is ln(2) ÷ ln(1 + r) for annual compounding. Rule of 70 note: at low rates (about 1%–4%) 70 ÷ rate is closer to the exact answer; from about 6% to 10%, 72 is closer. See the full 1%–20% table.
| Annual rate | Rule of 72 (years) | Rule of 70 (years) | Exact (years) |
|---|---|---|---|
| 1% | 72.00 | 70.00 | 69.66 |
| 2% | 36.00 | 35.00 | 35.00 |
| 3% | 24.00 | 23.33 | 23.45 |
| 4% | 18.00 | 17.50 | 17.67 |
| 5% | 14.40 | 14.00 | 14.21 |
| 6% | 12.00 | 11.67 | 11.90 |
| 7% | 10.29 | 10.00 | 10.24 |
| 8% | 9.00 | 8.75 | 9.01 |
| 9% | 8.00 | 7.78 | 8.04 |
| 10% | 7.20 | 7.00 | 7.27 |
| 11% | 6.55 | 6.36 | 6.64 |
| 12% | 6.00 | 5.83 | 6.12 |
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Use your actual figures where available. The output is an educational estimate based on the assumptions below.
Displayed amounts are rounded to two decimal places. Keep the same currency and time period across related inputs.
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How this Rule of 72 calculator works
The Rule of 72 estimates how many years it takes for money to double at a constant annual compound rate. Divide 72 by the annual percentage rate. An 8% return gives about 9 years; a 6% return gives about 12 years. This page also shows the exact doubling time from natural logarithms so you can see how close the shortcut is.
How to calculate the Rule of 72
- Find the annual compound rate as a percentage. Use an effective annual rate; if you only have a monthly-compounded nominal rate, convert it first (see below).
- Divide 72 by that rate. At 9% a year, 72 ÷ 9 = 8, so money doubles in about 8 years.
- Check or reverse it. For the exact figure, divide ln(2) by ln(1 + r): ln(2) ÷ ln(1.09) = 8.04 years. To find the rate needed to double in a set time, divide 72 by the years instead: doubling in 6 years needs about 72 ÷ 6 = 12% a year.
The doublings stack. At 8%, $10,000 doubles to about $20,000 in 9 years, $40,000 in 18 years and $80,000 in 27 years, assuming the rate holds and nothing is withdrawn. The CAGR calculator gives the exact rate for any start value, end value and number of years.
When to use this calculator
- Get a quick feel for how long compounding needs to double a balance at a stated rate.
- Compare rough doubling times across different assumed returns.
- Check the exact figure when the rate is far from the 6–10% band where the rule is most accurate.
How to use this calculator
- Enter an annual return rate as a percentage (for example 8 for 8%). Use an effective annual rate if you have one; otherwise treat the figure as a constant yearly compound rate.
- Read the Rule of 72 estimate in years, then compare it with the exact doubling time shown below.
- Remember that fees, taxes and changing markets are not modeled.
The formula
Exact years = ln(2) ÷ ln(1 + r) where r is the decimal rate
The shortcut works because 72 has many divisors and sits close to 100 × ln(2) ≈ 69.3, with a small adjustment that improves mid-range rates.
Worked example: doubling at 8%
At an 8% effective annual rate, the Rule of 72 says 72 ÷ 8 = 9.00 years to double. The exact calculation is ln(2) ÷ ln(1.08) ≈ 9.01 years. Starting with $10,000, you would expect about $20,000 after nine years of uninterrupted 8% growth with no contributions, taxes or fees.
At 12%, the rule gives 6.00 years while the exact figure is about 6.12 years — still close, but the gap widens as the rate moves away from the middle of the common band. At 2%, the rule gives 36 years while the exact figure is about 35.00 years.
Common mistakes
- Using a nominal rate with monthly compounding without converting to an effective annual rate first.
- Treating the result as a promise rather than a constant-rate illustration.
- Forgetting that withdrawals, fees and taxes lengthen the real path to a doubled balance.
- Applying the rule to simple interest (it is for compounding).
Reading the results
The headline is the Rule of 72 years. Exact doubling time uses natural logs for the same rate. Annual rate repeats your input, and Growth factor confirms the target is a 2× increase. Use the compound-interest or future-value calculators when you need a specific ending balance rather than a doubling time.
Choosing a rate to plug in
Use a rate that matches the question you are asking. For a diversified portfolio illustration, a long-run assumed return (after fees) is more honest than last year's peak. For cash or short bonds, a lower rate stretches the doubling time and shows why parking money in low-yield accounts grows slowly. If you only know a nominal rate with monthly compounding, convert to an effective annual rate first: EAR = (1 + nominal/12)12 − 1, then enter EAR × 100 in this tool.
The Rule of 72 is a teaching aid and a quick check, not a forecast. Markets do not deliver a constant percentage every year. Sequence of returns, contributions and withdrawals change the path. When you need a dollar target rather than a doubling time, switch to the compound-interest or savings-goal calculators and test a range of rates.
Sources
Related calculators
- CAGR calculator — the exact annual growth rate between two values, or the years to reach a target.
- Present value calculator — what a future amount is worth in today’s money.
- Inflation calculator — how rising prices change purchasing power.
- Dollar-cost averaging calculator — average cost when you invest a fixed amount on a schedule.
- ROI calculator — return on investment as a percentage of cost.
Related education
- Rule of 72 vs Rule of 70 (and the Rule of 69.3) — new guide with worked examples.
- How compound interest works — time, rate and contributions.
- Simple interest vs compound interest — why compounding matters for doubling.
- Future value — growing a starting amount to a target.
- Compound interest calculator · Future value calculator · Investment return calculator
Rule of 72 table: 1% to 20% (rule vs exact)
Years for money to double at a constant annual compound rate. "Exact" is ln(2) ÷ ln(1 + r). The last column is the Rule of 72 estimate minus the exact figure.
| Annual rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact | 72 minus exact |
|---|---|---|---|---|---|
| 1% | 72.00 | 70.00 | 69.30 | 69.66 | +2.34 |
| 2% | 36.00 | 35.00 | 34.65 | 35.00 | +1.00 |
| 3% | 24.00 | 23.33 | 23.10 | 23.45 | +0.55 |
| 4% | 18.00 | 17.50 | 17.32 | 17.67 | +0.33 |
| 5% | 14.40 | 14.00 | 13.86 | 14.21 | +0.19 |
| 6% | 12.00 | 11.67 | 11.55 | 11.90 | +0.10 |
| 7% | 10.29 | 10.00 | 9.90 | 10.24 | +0.04 |
| 8% | 9.00 | 8.75 | 8.66 | 9.01 | −0.01 |
| 9% | 8.00 | 7.78 | 7.70 | 8.04 | −0.04 |
| 10% | 7.20 | 7.00 | 6.93 | 7.27 | −0.07 |
| 11% | 6.55 | 6.36 | 6.30 | 6.64 | −0.10 |
| 12% | 6.00 | 5.83 | 5.77 | 6.12 | −0.12 |
| 13% | 5.54 | 5.38 | 5.33 | 5.67 | −0.13 |
| 14% | 5.14 | 5.00 | 4.95 | 5.29 | −0.15 |
| 15% | 4.80 | 4.67 | 4.62 | 4.96 | −0.16 |
| 16% | 4.50 | 4.38 | 4.33 | 4.67 | −0.17 |
| 17% | 4.24 | 4.12 | 4.08 | 4.41 | −0.18 |
| 18% | 4.00 | 3.89 | 3.85 | 4.19 | −0.19 |
| 19% | 3.79 | 3.68 | 3.65 | 3.98 | −0.20 |
| 20% | 3.60 | 3.50 | 3.46 | 3.80 | −0.20 |
Rule of 72 vs Rule of 70 vs Rule of 69.3
| Rule | Formula | Most accurate for |
|---|---|---|
| Rule of 72 | 72 ÷ rate | Annual compounding at roughly 6%–10%; easy mental maths (72 divides by 2, 3, 4, 6, 8, 9, 12) |
| Rule of 70 | 70 ÷ rate | Low rates such as 1%–4%, and economic growth or inflation rates |
| Rule of 69.3 | 69.3 ÷ rate | Continuous compounding, where it is exact: ln(2) ≈ 0.693 |
Frequently asked questions
Is the Rule of 72 exact?
No. It is a rule of thumb. This page also shows the exact years using natural logs so you can compare.
What if my return changes every year?
The rule assumes a constant annual rate. Variable returns need a different model such as CAGR from start and end values.
How do you calculate the Rule of 72?
Divide 72 by the annual percentage rate. At 6%, 72 ÷ 6 = 12 years to double. Use the rate as a whole number, not a decimal.
What is the Rule of 70?
The same shortcut using 70 instead of 72: years to double ≈ 70 ÷ rate. It is a little more accurate at low rates, such as 1%–4%, and is often used for GDP growth and inflation.
What is the Rule of 69.3?
69.3 ÷ rate. It is exact for continuous compounding, because ln(2) ≈ 0.693. For annual compounding, 72 is usually closer at typical investment returns.
Can the Rule of 72 be used for inflation?
Yes. Divide 72 by the inflation rate to estimate how long it takes prices to double, or for money to lose half its purchasing power. At 3% inflation that is about 24 years.
What does the Rule of 72 table show?
For each annual rate, it shows about how many years money takes to double: 72 divided by the rate, next to the exact figure ln(2) ÷ ln(1 + r). At 6% the rule gives 12.0 years and the exact answer is 11.9.
Can the Rule of 72 work out the rate needed to double?
Yes. Divide 72 by the number of years. To double in 6 years you need about 72 ÷ 6 = 12% a year.
Worked example: how long does $5,000 take to double at 6%?
72 ÷ 6 = 12 years to reach about $10,000. The exact answer is ln(2) ÷ ln(1.06) ≈ 11.9 years.
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