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Rule of 70 Calculator

Estimate doubling time with the rule of 70.

How it is calculated

The rule of 70 estimates how long a quantity growing at a steady percentage rate takes to double: years ≈ 70 ÷ r, where r is the annual growth rate in percent (enter 4 for 4%, not 0.04). The rate must be above zero; zero or negative rates return no result. The answer is in years with two decimals. It works because ln 2 ≈ 0.693, which is close to 0.70 when the rate is expressed as a percentage. It is an approximation: the exact doubling time at 4% is 17.67 years, and the shortcut is most accurate at low rates. It assumes compounding once a year and a constant rate.

Worked example

An investment grows 4% per year. Divide 70 by 4 to get 17.50 years as the estimated doubling time. The exact answer, ln 2 ÷ ln 1.04, is about 17.67 years, so the shortcut is off by about two months. At 7% growth, 70 ÷ 7 gives 10 years.

Try this example →

Common mistakes

  • Entering the rate as a decimal. Typing 0.04 gives 1,750 years because the rule expects 4.
  • Using it for a rate that changes from year to year. The rule needs one constant average rate.
  • Applying it to very high growth rates, such as 50% or more, where the approximation drifts noticeably from the exact result.
  • Forgetting inflation. A 4% nominal return with 3% inflation doubles purchasing power far slower than 17.5 years.
  • Using it for shrinking quantities. The tool rejects negative rates, so use a halving-time calculation instead.

Sources

About this calculator

The rule of 70 is a mental-math shortcut for estimating doubling time: divide 70 by the annual growth rate (as a percentage) to get roughly how many years it takes a quantity to double. It comes from the natural-log identity ln(2) ≈ 0.693, so the exact doubling time is ln(2)/r; multiplying by 100 to convert r from a decimal to a percentage gives 69.3/r, which rounds to 70 because 70 divides evenly by more small numbers (2, 5, 7, 10) than 69.3 does, making the mental arithmetic easier.

Economists use it to estimate how long it takes GDP or a population to double at a given growth rate, and to gauge how fast inflation erodes purchasing power (the “doubling” of prices, or halving of what money buys); biologists use it for bacterial or cell-culture growth; and investors use it as a quick sanity check on compound-interest projections alongside the closely related rule of 72.

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Comments (1)

  • Editorial team

    Prices make a good use of this rule. At 3% inflation, 70 ÷ 3 gives about 23.33 years for prices to double, so what a given amount buys halves in about that time; at 6% it is about 11.67 years. Because the rule assumes one constant rate, try a low and a high rate to bracket the answer. Which quantity are you tracking, savings, prices, a population or something else?

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