Rule of 70 Doubling Time Calculator
Estimate how long it takes a quantity to double at a constant growth rate using the Rule of 70, and compare it with the exact doubling time.
How it works
Doubling time ≈ 70 / (growth rate %) · Exact = ln 2 / ln(1 + rate)
The Rule of 70 is a fast mental shortcut: divide 70 by the percentage growth rate to estimate how many periods a quantity takes to double. It works because ln 2 ≈ 0.693, and 69.3 rounds to a conveniently divisible 70. The rule is most accurate at low single-digit rates and drifts a little from the exact logarithmic answer as the rate climbs.
Worked example
At 7% growth, the Rule of 70 gives 70 / 7 = 10 periods to double. The exact figure is ln 2 / ln 1.07 = 0.6931 / 0.0677 = 10.24 periods, so the shortcut is off by only about a quarter of a period.
Sources: Rule of 72 — Wikipedia
Frequently asked questions
Should I use the Rule of 70 or the Rule of 72?
Both estimate doubling time; 72 is often preferred for interest because it divides cleanly by many rates, while 70 is closer to the exact ln 2 constant and is common in population and economics contexts. The difference between them is tiny for typical rates.
How accurate is the Rule of 70?
Very accurate for low rates. At 2–3% the error is well under half a period; by 15–20% the approximation increasingly overstates the true doubling time, so use the exact logarithmic formula for large rates.
Does it work for shrinking quantities?
The rule is built for positive growth and doubling. For decay you would instead compute a half-life; this calculator requires a positive growth rate so it never divides by zero.
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Educational financial-math tool, not investment or financial advice.