Doubling Time Calculator

Find how long it takes for a quantity to double at a constant growth rate — or find the growth rate needed to double in a given time.

Growth rate per period

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Exact (ln formula)

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Rule of 70 approx.

FAQ

What is the Rule of 70? ›

The Rule of 70 is a mental math shortcut: divide 70 by the growth rate (%) to estimate the doubling time. At 7% growth, it doubles in approximately 70 ÷ 7 = 10 periods. It's an approximation of the exact formula ln(2) ÷ ln(1 + r), and is accurate for rates under about 10%.

What is the exact doubling time formula? ›

Exact Doubling Time = ln(2) ÷ ln(1 + r/100), where r is the growth rate as a percentage. For continuous compounding: ln(2) ÷ r. The logarithm base doesn't matter as long as you're consistent.

Why does the Rule of 70 work? ›

ln(2) ≈ 0.693, and for small rates ln(1+r) ≈ r. So doubling time ≈ 0.693/r ≈ 69.3/r%. Rounding to 70 makes mental math easy. Some use the Rule of 72 instead, which is more accurate for rates around 6–10%.

About this calculator

Doubling time is used in finance (compound interest), biology (population growth), economics (GDP growth), and physics (radioactive decay half-life is the inverse concept). This calculator shows both the exact result using logarithms and the Rule of 70 approximation.