Doubling Time Calculator
Enter a growth rate per period to find how long it takes for the amount to double.
Doubling time is how long something growing at a constant rate takes to double. The exact figure is the natural log of 2 divided by the natural log of one plus the rate. The Rule of 72 gives a quick estimate: divide 72 by the percentage growth rate.
How to Use This Calculator
Enter the constant growth rate as a percentage for one period. The period can be anything — a year for an investment, a day for a population — and the answer comes out in the same units. For a savings account growing 6% a year, enter 6 and read the answer in years.
The calculator shows two numbers: the exact doubling time from the logarithmic formula, and the Rule of 72 estimate. Comparing them shows why the shortcut is popular and where it drifts.
How the Calculation Works
Anything growing at a fixed percentage each period grows exponentially. Solving the compound-growth equation for the time when the amount reaches twice its start gives the exact formula: the natural logarithm of 2 divided by the natural logarithm of one plus the rate written as a decimal.
The Rule of 72 is an approximation of that formula. Dividing 72 by the percentage rate gives a close estimate for the mid-single-digit rates common in finance, and it is easy to do in your head.
doubling time = ln(2) ÷ ln(1 + rate)
Worked Example
At a 6% annual growth rate, the exact doubling time is ln(2) ÷ ln(1.06) = 0.6931 ÷ 0.05827 = 11.90 years.
The Rule of 72 estimate is 72 ÷ 6 = 12 years. The shortcut is within a tenth of a year here, which is why it is trusted for quick mental math around 6–10%.
What the Result Means
The exact figure tells you precisely how many periods until the amount doubles at that steady rate. It is the honest number to use for planning. The Rule of 72 is a sanity check you can do without a calculator.
The two diverge at the extremes: at very high rates the Rule of 72 overstates the time, and some people switch to 70 or 69.3 for continuous compounding. For everyday interest rates, 72 is the sweet spot.
Assumptions and Limitations
- Assumes a constant growth rate every period — real returns vary
- The rate and the answer share the same period (annual rate → years)
- The Rule of 72 is an approximation, most accurate around 6–10%
- Does not account for fees, taxes or withdrawals
When to Use a Doubling Time Calculator
Investors, savers, and students use this to see how long money — or anything growing at a steady rate — takes to double. Enter a growth or interest rate to apply both the Rule of 72 and the exact formula, whether you are comparing investment returns, projecting a savings balance, or studying compound growth. It turns an abstract percentage into a concrete number of years you can plan around.
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Open calculator →Frequently Asked Questions
What is the Rule of 72?
It is a shortcut for doubling time: divide 72 by the percentage growth rate. At 8%, money doubles in about 72 ÷ 8 = 9 years. It is an approximation of the exact logarithmic formula.
How accurate is the Rule of 72?
Very accurate for rates around 6–10%, usually within a fraction of a period. It drifts at very high or very low rates, where the exact ln(2) ÷ ln(1 + rate) formula is better.
What is the exact doubling time formula?
Doubling time equals the natural log of 2 divided by the natural log of one plus the rate as a decimal. At 6%, that is 0.6931 ÷ 0.0583 = 11.9 years.
Can I use this for things other than money?
Yes. Any quantity growing at a constant percentage — population, users, bacteria — doubles on the same schedule. Enter the rate per period and read the answer in those periods.
Why do some people use 70 instead of 72?
Seventy (or 69.3) is closer for continuous compounding because ln(2) is about 0.693. Seventy-two is preferred for annual compounding because it divides cleanly by many common rates.
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