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Doubling Time Calculator

See how many periods it takes to double or triple at a compound growth rate.

How it is calculated

For a growth rate of r per period (entered as a percentage), compounding gives a doubling time of t = ln(2) / ln(1 + r) and a tripling time of ln(3) / ln(1 + r), with r = rate / 100. This is the exact answer from the compound-growth formula.

The tool also shows the Rule of 72 shortcut, 72 / rate, a mental-arithmetic estimate that is close for moderate rates (roughly 4% to 12%) and drifts for very small or very large ones. The rate must be above zero, since zero growth never doubles. Results are in the same period as the rate: a yearly rate gives years, a monthly rate gives months. The tool labels all results with the generic period label, so read it in your own unit.

Worked example

An investment grows 7% per period. Doubling time is ln(2) / ln(1.07) = 0.6931 / 0.0677 = 10.24 years. Tripling takes ln(3) / ln(1.07) = 16.24 years. The Rule of 72 estimate is 72 / 7 = 10.29 years, only about 0.05 off the exact figure.

Try this example →

Common mistakes

  • Typing 0.07 instead of 7 for the rate; the tool expects a percentage.
  • Treating the Rule of 72 as exact. It is an approximation, and at high rates it differs noticeably from the exact value.
  • Forgetting that the answer is in periods. With a monthly rate, 10 means 10 months, not 10 years.
  • Applying it to a rate that changes over time; the formula assumes the same rate every period.

About this calculator

This calculator finds how many periods it takes an amount to double or triple at a given compound growth rate, using t = ln(2)/ln(1+r) for doubling and t = ln(3)/ln(1+r) for tripling, and also shows the quick mental-math shortcut, the Rule of 72 (72 ÷ rate ≈ years to double).

Investors and savers use it to see how long it takes a portfolio, savings account, or any compounding quantity to grow, and to compare the real math against the Rule of 72 approximation people often quote from memory.

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