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Constant-Growth Doubling Time Calculator

Find the logarithmic doubling time for a constant positive compound growth rate, or solve for the growth rate.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

At 100% growth per period, a quantity doubles in one period. This calculator uses logarithms, so it gives 1 rather than the 0.72 produced by the rough 72/r shortcut.

Doubling time = ln(2) / ln(1 + growth rate per period)

Worked example

Enter these known values and leave the other values blank.

Compound growth rate per period
100 % /period
Doubling time in matching periods
1 periods

Assumptions and limitations

  • The growth rate is constant and positive, with no withdrawals, extra contributions or other changes. This describes a mathematical growth path rather than a forecast.
  • Time is measured in the same periods as the rate. Fractional times use continuous interpolation of the discrete compound-growth formula. Zero or negative growth does not give a finite future doubling time.

Common questions

Is this the Rule of 72 shortcut?

The source catalog calls it Rule of 72, but the working equation is the exact constant-growth logarithmic formula. The shortcut 72 divided by the percentage rate is only an approximation.

Does the output always mean years?

Only when the input rate is per year. A monthly growth rate produces a doubling time in months.

References

Bookify adds explicit model-domain checks: A finite future doubling time requires positive growth. The future doubling time must be positive.

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