Finance
Rule of 72 Calculator
Years to double at a constant annual rate.
Free to use — no sign-up or login.
Years to double
Amortization schedule
| # | Date | Payment | Principal | Extra | Interest | Balance |
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The Rule of 72 is a mental shortcut for compounding: divide 72 by an annual rate in percent to estimate how many years a balance takes to double if that rate stays constant. Enter the rate once; the calculator returns years to double. It is an approximation built for quick checks, not a full compound-interest schedule.
For exact growth of a present amount, use the Compound Interest Calculator or Future Value Calculator. To recover an annualized rate from a start and end value, use CAGR. The teaching walkthrough is How to Use the Rule of 72.
Why 72?
Continuous compounding doubles in about ln(2)/r ≈ 0.693/r years when r is a decimal rate. Multiplying by 100 to work in percent gives roughly 69.3 / (percent rate). The number 72 is a nearby integer that divides cleanly by common rates (3, 4, 6, 8, 9, 12) and stays close enough for moderate annual rates. Related shortcuts use 69 or 70; this page implements 72 ÷ rate only.
When the shortcut drifts
Accuracy is best for steady positive rates in a middle band (often cited around roughly 6–10%). Very low or very high rates, intra-year compounding that differs from the annual rate you typed, fees, and changing returns all move the true doubling time. Treat the output as a planning estimate you can cross-check with compound interest when the decision matters.
Worked example: 8% annual rate
The default annual rate is 8%. Years to double ≈ 72 / 8 = 9 years exactly under the shortcut. A rough check with annual compounding: (1.08)^9 ≈ 1.999, which is essentially a double. At 6%, the rule gives 72 / 6 = 12 years; at 12%, it gives 6 years.
\[ t\approx\frac{72}{8}=9 \]
Frequently asked questions
Do I enter 8 or 0.08 for an 8% rate?
Enter 8. The field is annual rate in percentage points, matching everyday “8%” language.
Is this the same as exact compound-interest doubling time?
Not exactly. Exact doubling under annual compounding solves (1 + r/100)^t = 2 for t. The Rule of 72 approximates that t. For precise schedules, open the compound-interest or future-value tools.
Does the rule work for cutting a value in half?
People sometimes reuse similar shortcuts for halving under decay, but this calculator only reports years to double from a positive growth rate. It is not a half-life tool.
What if the rate is zero or negative?
The shortcut needs a positive rate. Zero or negative rates do not produce a finite doubling time under this rule.
Sources
Assumptions and limitations
Finance results are illustrative. They typically omit taxes, fees, prepayment penalties, and product rules, and they are not investment or lending advice.
Years ≈ 72 ÷ rate% assumes a constant positive annual rate and is an approximation. It ignores fees, taxes, contributions, and changing returns. Illustrative only — not investment advice.