Calculator Tools
Rule of 72 Calculator
Estimate how long money takes to double with the Rule of 72, plus the exact ln(2)/ln(1+r) value, Rule of 70, Rule of 69.3, and inflation halving time.
Rule of 72 calculator
Enter an interest or growth rate to estimate how long it takes a balance to double.
Inputs
Enter the rate as a percent. 8 means 8% per year, compounded annually.
Used only to show what the balance grows into. Leave blank to skip.
Doubling time
Rule of 72 estimate
9 years
72 / 8% per year
- Exact doubling time
- 9.006 years
ln(2) divided by ln(1 + r). The textbook value.
- Rule of 72
- 9 years
Drift vs exact: -0.07%
- Rule of 70
- 8.75 years
Drift vs exact: -2.85%
- Rule of 69.3
- 8.664 years
Drift vs exact: -3.80%
- Time to triple
- 14.275 years
Rule of 114 quick estimate: 14.25 years
- Time to quadruple
- 18.013 years
Rule of 144 quick estimate: 18 years
Starting amount $10,000.00
Doubles to $20,000.00 in 9.01 years at 8% per year.
Growth path to doubling
A smooth compound curve at 8% per year. Real-world returns vary year to year; this table shows the idealized path.
| Year | Balance | Multiple |
|---|---|---|
| 0 | $10,000.00 | 1x |
| 0.9 | $10,717.73 | 1.0718x |
| 1.8 | $11,486.98 | 1.1487x |
| 2.7 | $12,311.44 | 1.2311x |
| 3.6 | $13,195.08 | 1.3195x |
| 4.5 | $14,142.14 | 1.4142x |
| 5.4 | $15,157.17 | 1.5157x |
| 6.3 | $16,245.05 | 1.6245x |
| 7.21 | $17,411.01 | 1.7411x |
| 8.11 | $18,660.66 | 1.8661x |
| 9.01 | $20,000.00 | 2x |
Rule of 72 vs exact at common rates
The Rule of 72 hugs the exact doubling curve most closely between 6% and 10%. At higher rates the approximation overstates the time slightly; at very low rates the Rule of 70 (or 69.3) is closer.
| Rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact | Rule 72 drift |
|---|---|---|---|---|---|
| 1% | 72 years | 70 years | 69.31 years | 69.66 years | +3.36% |
| 2% | 36 years | 35 years | 34.66 years | 35 years | +2.85% |
| 3% | 24 years | 23.33 years | 23.1 years | 23.45 years | +2.35% |
| 4% | 18 years | 17.5 years | 17.33 years | 17.67 years | +1.85% |
| 5% | 14.4 years | 14 years | 13.86 years | 14.21 years | +1.36% |
| 6% | 12 years | 11.67 years | 11.55 years | 11.9 years | +0.88% |
| 7% | 10.29 years | 10 years | 9.9 years | 10.24 years | +0.40% |
| 8% | 9 years | 8.75 years | 8.66 years | 9.01 years | -0.07% |
| 9% | 8 years | 7.78 years | 7.7 years | 8.04 years | -0.54% |
| 10% | 7.2 years | 7 years | 6.93 years | 7.27 years | -1.00% |
| 12% | 6 years | 5.83 years | 5.78 years | 6.12 years | -1.90% |
| 15% | 4.8 years | 4.67 years | 4.62 years | 4.96 years | -3.22% |
| 20% | 3.6 years | 3.5 years | 3.47 years | 3.8 years | -5.31% |
| 25% | 2.88 years | 2.8 years | 2.77 years | 3.11 years | -7.28% |
Why 72?
The exact doubling time at rate r is ln(2) divided by ln(1 + r). For small r, ln(1 + r) is approximately equal to r, so the formula reduces to ln(2) / r, which is roughly 0.693 / r. Multiplied by 100 to align with percent notation, that gives 69.3 / r. 72 is preferred in finance because it is close to 69.3, falls between the discrete and continuous compounding constants, and divides evenly by 2, 3, 4, 6, 8, 9, and 12, which makes the mental math fast.
Rule of 70 vs Rule of 72 vs Rule of 69.3
All three estimate the same quantity. The Rule of 69.3 is the continuous-compounding limit and is the most accurate for very small rates. The Rule of 70 is the most common shortcut in academic and government inflation reports. The Rule of 72 is the most accurate for interest rates between roughly 6% and 10%, the range most often quoted for retirement planning, which is why it is the default in personal finance.
Triple and quadruple
The same shortcut generalizes. To estimate the time to triple at a constant rate, divide 114 by the rate percent (a rounded form of 100 times ln(3), which is 109.9). To estimate the time to quadruple, divide 144 by the rate percent (a rounded form of 100 times ln(4), which is 138.6). The Years to double mode shows both the exact and the back-of-envelope value side by side.
What the rule does not include
The Rule of 72 assumes a constant rate, annual compounding, and no contributions or withdrawals. Real returns vary year to year and taxes, fees, dividends paid out, and currency effects all change the answer. Treat the result as a fast sanity check, not a forecast. For a series of cash flows, use a compound interest or NPV and IRR calculator instead.
How to use
- Pick a mode at the top: Years to double (rate to time), Required rate (target years to rate), or Halving (inflation to halving time).
- For Years to double, enter an annual rate as a percent and optionally a starting balance to see how much it grows into.
- For Required rate, enter the number of years you want a balance to double in and read the rate the Rule of 72, Rule of 70, Rule of 69.3, and the exact formula each suggest.
- For Halving, enter an inflation rate to estimate how long one unit of currency takes to lose half its purchasing power.
- Click a preset chip to load a real-world scenario (stock index, savings, double in 10 years, double in 7 years, 3 percent or 7 percent inflation), and use Copy summary to paste the result into a deal memo or savings plan.
About this tool
Rule of 72 Calculator estimates how long money takes to double at a constant compound rate, and turns that estimate around to find the rate required to double in a target horizon. The Rule of 72 itself is the shortcut years to double is approximately 72 divided by the rate in percent, so a balance growing at 8 percent per year doubles in roughly 9 years and a balance growing at 6 percent doubles in roughly 12 years. The tool shows three answers at once: the Rule of 72 estimate, the Rule of 70 (which textbooks favor for low rates), the Rule of 69.3 (which is the continuous-compounding limit, 100 times ln(2)), and the exact closed-form value ln(2) divided by ln(1 + r). The drift between the approximation and the exact answer is surfaced explicitly so you can see why the Rule of 72 is the right shortcut for retirement-account rates (6 to 10 percent) and why the Rule of 70 wins for low single-digit inflation. A second mode inverts the question: enter the years you want and the calculator returns the rate that doubles a balance in that horizon, computed as 2 to the power of (1 divided by years), minus 1, with the three shortcut estimates and their drift shown alongside. A third mode applies the same math to inflation: enter an annual price-level growth rate and the tool reports how long it takes one unit of currency to lose half of its purchasing power, with an optional balance and a year-by-year decay table so the abstraction becomes a real number you can paste into a memo. The tool also shows time to triple at the same rate (Rule of 114) and time to quadruple (Rule of 144), and a comparison table that walks the Rule of 72 estimate against the exact value at every common rate from 1 percent through 25 percent. All math runs in your browser, so the rates, balances, and projections you analyze never leave your device.
Free to use. Works in your browser. No signup, no login.
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