Updates automatically as you type.
Calculated in your browser; your inputs are not sent to us. Privacy
Calculation details
Review the generated output before relying on it.
This tool runs in your browser. Your calculator inputs and results are never transmitted to us or to ad/affiliate partners. Ads and sponsored links may set third-party cookies to serve and measure them, but they never receive your calculation values. If you explicitly save a scenario, its permitted fields stay in local browser storage until you clear them. See our Privacy Policy.
Use this result
Share the current inputs or ask ChatGPT to explain the calculation in context.
More options
How This Tool Works
Calculation Method
Computes Doubling time from Annual rate.
Site methodology
No unrelated authority link is added merely to make this page look sourced. Tool-specific external sources are shown only when they directly support the method, rate, or rule.
Assumptions to Verify
- Rates, fees, timing, and rules can change.
- Use the result as a planning estimate and verify current terms.
Privacy: The calculation runs in this browser. Shared links contain the page address only, not your inputs or results.
Years to double at each rate
What this means for your numbers: The worked example shows the same 72 dividing three ways: 9 years for investments, 24 for inflation, 6 for credit-card debt. The rule is one number applied to opposite sides of your balance sheet.
Illustrative breakdown using the worked example above. The calculator computes your own numbers with the same formula.
Where the 72 Comes From, Worked at 9 Percent and 6 Percent
The shortcut exists because ln(2) is about 0.693, and the natural log of (1 + r) for small r is roughly r itself, so the true doubling time ln(2) / ln(1 + r) approximates 0.693 / r. Multiplying numerator and denominator by 100 to work in percent gives 69.3 / r, and 72 is chosen over 69.3 because it divides cleanly by 3, 4, 6, 8, 9, and 12, which are the rates people actually quote. That small upward tweak is why the rule reads slightly optimistic in the middle of its range.
Worked example at 9 percent: the rule gives 72 / 9 = 8.0 years. The exact answer is ln(2) / ln(1.09) = 0.6931 / 0.0862 = 8.04 years, so the shortcut is about 0.04 years low, an error under 1 percent. At 6 percent: 72 / 6 = 12.0 years by the rule, versus ln(2) / ln(1.06) = 0.6931 / 0.0583 = 11.90 years exact, about 0.10 years high. Both land within a rounding error, which is why 5 to 10 percent is the sweet spot. Push to 3 percent and the gap widens to 24.0 versus 23.45 years, and at 12 percent it is 6.0 versus 6.12, the rule now on the low side again.
Boundary Cases: 0 Percent, the 30 Percent Cap, and Negative Rates
At exactly 0 percent the rule has no answer, and neither does the exact formula, because nothing compounds: ln(1) is 0 and dividing by it is undefined. The calculator treats 0 as an invalid input for that reason. A rate so small it prints as 0.0 percent still slips through, and the honest output is enormous: 0.5 percent gives 72 / 0.5 = 144 years by the rule, versus 138.98 exact. Cheap savings accounts sit here, which is the useful takeaway: at 0.5 percent a balance doubles roughly twice per working lifetime.
At the 30 percent cap the rule reads 72 / 30 = 2.4 years, but the exact answer is ln(2) / ln(1.30) = 0.6931 / 0.2624 = 2.64 years. The shortcut is now about 0.24 years, or 9 percent, optimistic, because ln(1.30) is meaningfully smaller than 0.30. The gap grows faster than linear from here: at 72 percent the rule says 1.0 year while compounding says 1.31. Negative rates behave in a way the mental shortcut was never built for: at minus 2 percent, 72 / (-2) = -36 years, and the exact answer is -34.31 years, meaning a balance falling 2 percent a year is cut in half in about 34 years. The negative sign flips the meaning from doubling to halving, which is the one insight the rule still survives, but the number only holds for small negative rates where ln(1 + r) stays roughly linear.