Softonic

Doubling Time Calculator

Step 1 / 3 Exact doubling time
Next

Anything that grows at a steady percentage rate doubles on a fixed schedule, whether it is an investment compounding at 7% a year, a population, website traffic or bacteria in a dish. This calculator turns a single growth rate into a doubling time three ways: the exact logarithmic answer, the classroom Rule of 70 and the investor-friendly Rule of 72. Enter a rate, pick a period, and read all three side by side.

How to find a doubling time

  1. 1

    Enter the growth rate

    The constant percentage increase per period. 7% per year is a common long-run stock-market assumption; use whatever rate fits your scenario.

  2. 2

    Choose the period

    Years, months or days. This is a label only: it tells you the units of the answer, since the math is the same whatever the period.

  3. 3

    Read the three answers

    The exact doubling time (from logarithms), plus the Rule of 70 and Rule of 72 quick estimates, all expressed in the same periods you chose.

The formula

For a quantity growing at a constant rate r per period, the exact doubling time is the number of periods t that satisfies (1 + r)^t = 2. Solving with logarithms:

t = ln(2) / ln(1 + r)

where r is the growth rate as a decimal (7% → 0.07). The Rule of 70 and Rule of 72 are shortcuts that skip the logarithm:

  • Rule of 70: t ≈ 70 / growth%
  • Rule of 72: t ≈ 72 / growth%

Here the rate is written as a whole percentage (7, not 0.07). The number 70 comes from ln(2) × 100 ≈ 69.3, rounded up for easier mental math; 72 is preferred because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12.

A worked example

Suppose your portfolio grows 7% per year. The exact answer is ln(2) / ln(1.07) = 0.6931 / 0.0677 = 10.24 years. The Rule of 70 gives 70 / 7 = 10.0, and the Rule of 72 gives 72 / 7 = 10.29. All three land within a quarter of a year of each other.

How the estimates compare

Growth rate Exact (ln) Rule of 70 Rule of 72
2% 35.00 35.00 36.00
5% 14.21 14.00 14.40
7% 10.24 10.00 10.29
10% 7.27 7.00 7.20
15% 4.96 4.67 4.80

The two rules are most accurate near 8% and drift apart from the exact value at very high rates, where the logarithm matters more.

Common pitfalls

  • Mixing up the rate format. The exact formula uses a decimal (0.07); the two rules use the whole number (7). The calculator handles both for you.
  • Assuming the rate is constant. Real returns, inflation and traffic all vary year to year. A doubling time is only as reliable as the steady rate you feed it.
  • Confusing the period. A 7% monthly rate doubles in ~10 months, not 10 years. The label you pick is the unit of the answer.

Frequently Asked Questions

Both are estimates of the same thing. The Rule of 70 is slightly closer to the true value at low rates and is common in economics; the Rule of 72 is favoured in finance because 72 divides evenly by so many numbers, making mental math easy. For an accurate figure, use the exact logarithmic result shown alongside them.

The exact doubling time comes from solving (1 + r)^t = 2 with natural logarithms. The two rules approximate that logarithm with a fixed numerator (70 or 72). They agree closely around 8% and diverge at very high or very low rates.

No. The doubling time depends only on the per-period growth rate. The period you select is a label that tells you the units of the answer: a 7% per-year rate doubles in about 10 years, while a 7% per-month rate doubles in about 10 months.

No. Nothing you enter is stored, saved or shared. The growth rate and period are sent to our servers only to run the calculation, and they may be carried in the page link as you move through the steps.

Related Tools

BMI Calculator

Calculate body mass index from height and weight. Shows WHO category, healthy-weight range and limitations of BMI.

Social Security Calculator

Estimate a US Social Security retirement benefit from your PIA and claiming age. Compare monthly and annual amounts at 62, FRA 67 and 70.

Age Calculator

Calculate exact age in years, months and days from a birth date, plus total days, hours and the next birthday countdown.

Dog Age Calculator

Convert your dog's age to human years using modern veterinary research. Breed-size aware: small, medium and large dogs age differently.

Amp-Hour Calculator

Work out battery runtime and stored energy from amp-hours, voltage and load current. Get runtime in hours and minutes plus energy in watt-hours and kilowatt-hours.

Fahrenheit to Celsius Converter

Convert Fahrenheit temperatures to Celsius with the exact formula, Kelvin output and common reference points for weather, cooking and health.

Tool available in other languages