Rule of 72 Calculator
Estimate how long steady compound growth takes to double, then compare the mental-math rule with the exact logarithmic result.
Growth assumptions
Doubling-time results
Method comparison
| Method | Formula | Doubling time | Difference from exact |
|---|---|---|---|
| Exact compound growth | ln(2) / ln(1 + r) | 9.01 years | 0.00 years |
| Rule of 72 | 72 / 8 | 9.00 years | – 0.01 years |
How to use the Rule of 72 calculator
What this calculator does
This calculator estimates the number of equal periods required for a quantity to double when it grows at one constant compound rate. It shows both the familiar Rule of 72 shortcut and the exact logarithmic doubling time, so you can see how close the shortcut is for the rate you entered. The model is useful for investments, prices, revenue, users, traffic, production, or any other quantity that compounds by the same percentage each period. It does not predict an actual investment return, account for volatility, taxes, fees, contributions, withdrawals, or guarantee that a rate will continue.
When to use it
Use it to make a quick reasonableness check on a long-term growth assumption, compare two proposed growth rates, translate a target rate into a time horizon, or explain compounding in a budget or planning discussion. For formal investment projections, pair this estimate with a full compound-interest model and realistic scenario ranges.
How to calculate
- The calculator opens with a ready-to-use 8% annual-growth demonstration and an immediately available example XLSX workbook.
- Replace Increase per period with a positive percentage. You may type 8, 8.5, or 8%; grouped numbers, scientific notation, negative values, and decimal commas are rejected.
- Choose the Period unit. The unit labels the answer but does not convert the rate. An 8% monthly rate produces an answer in months; an 8% yearly rate produces an answer in years.
- Read Exact doubling time for the compound-growth result, then compare it with Rule of 72 estimate, Estimate error, and Relative error.
- Select Download Excel to export the current validated inputs and results. Reset clears the demonstration values and results; export is then disabled until a complete valid state is entered again.
Input guide
Increase per period is required and accepts a positive percentage greater than 0 and no more than 1,000,000%. A realistic example is 8%. Raising the rate shortens the doubling time; lowering it lengthens the time. Do not enter 0 for “no growth,” and do not enter 0.08 when you mean 8% – this field expects percentage points. Period unit is required and accepts Years, Months, Weeks, Days, or Periods. It controls wording only, because the entered rate and resulting time must use the same period.
Output guide
Exact doubling time is the estimated count of periods from the logarithmic compound-growth identity. Rule of 72 estimate is the mental-math approximation 72 divided by the percentage rate. Estimate error is shortcut minus exact time, while Relative error expresses that difference as a percentage of exact time. A negative error means the shortcut slightly understates the required time. Growth factor at exact time is an identity check and should be 2.0000×. The summary pills repeat the selected rate and both principal time estimates. The method comparison table shows the same two methods, formulas, doubling times, and differences from exact.
Worked example
At the startup value of 8% per year, the exact calculation is ln(2) ÷ ln(1.08) = 9.0065, displayed as 9.01 years. The Rule of 72 gives 72 ÷ 8 = 9.00 years. The shortcut error is about – 0.01 years, or – 0.13% relative to the exact result.
Learn more
The U.S. Securities and Exchange Commission explains the mechanics of compound interest, while FINRA describes the Rule of 72 as a quick estimating tool. For inflation comparisons, the U.S. Bureau of Labor Statistics provides the Consumer Price Index overview.
How the formula works
Compound growth follows future = present × (1 + r)^t. Doubling means the future-to-present ratio equals 2, so solving for time gives t = ln(2) / ln(1 + r). The Rule of 72 replaces that logarithmic calculation with a convenient numerator that is easy to divide by many common rates. It is usually close for moderate positive rates, but its error becomes more noticeable at unusually low or high rates.
Interpreting the estimate responsibly
Constant growth is the key assumption. Market returns, business growth, and inflation rarely repeat at exactly the same rate, so the result is best treated as a clean benchmark rather than a promise. Compare a base case with conservative and optimistic rates, and remember that a loss requires a larger subsequent gain to recover. For example, a 50% loss requires a 100% gain to return to the starting value.