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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.

Sources

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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Comments (1)

  • Editorial team

    A practical use is inflation. Enter 3 and the exact doubling time is 23.45 periods, so prices double in about 23 years if the rate holds; the Rule of 72 gives 24. For savings, enter a rate after inflation and tax, otherwise the result describes your balance, not your buying power. The result is labelled in years, but it really is in whatever period your rate uses, so a monthly rate gives months. What growth rate are you checking, and over what period?

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