Rule of 72 Calculator
The mental shortcut, checked against the exact answer.
Work out Rule of 72. The mental shortcut, checked against the exact answer. Says which constants are exact and which are conventions.
Years to double (rule of 72)
9
Exact answer 9.0065 · off by 0.072%
The exact doubling time is ln(2) ÷ ln(1 + r). The rule works because ln(2) is 0.693 and, for small rates, ln(1+r) ≈ r — so 69.3 is the mathematically natural numerator. 72 is used instead because it compensates for the curvature at ordinary rates and divides evenly by 2, 3, 4, 6, 8, 9 and 12, which matters when the whole point is doing it in your head. At 8.00% the exact numerator would be 72.05, and the rule is off by 0.07%.
How the Rule of 72 Calculator works
The exact doubling time is ln(2) ÷ ln(1 + r). The rule works because ln(2) is 0.693 and, for small rates, ln(1+r) is roughly r — so 69.3 is the natural numerator. 72 is used because it compensates for the curvature and divides evenly by far more numbers.
Also known as: doubling time calculator · how long to double my money · rule of 70 calculator · rule of 72 formula
Where 72 comes from
The exact doubling time is ln(2) ÷ ln(1 + r). Since ln(2) is 0.693 and, for small r, ln(1+r) is approximately r, the natural numerator is 69.3.
72 is used instead for two reasons. It compensates for the curvature that the approximation ignores, making it more accurate in the 6–10% range where it is usually applied. And it divides evenly by 2, 3, 4, 6, 8, 9 and 12 — which matters a great deal when the entire point is doing it in your head.
How far it drifts
At 8% the rule gives 9 years against an exact 9.006 — an error under a tenth of a percent.
At 25% it gives 2.88 against an exact 3.11, which is off by more than 7%. The approximation degrades as rates rise, because ln(1+r) diverges further from r.
This page shows the numerator that would have been exact at your rate, which makes the drift visible rather than theoretical.
Frequently asked questions
What is the rule of 72?
Divide 72 by the percentage rate to estimate the years to double. At 8% that gives 9 years, against an exact 9.006.
How accurate is it?
Very, in the 6–10% range where it is usually applied — within a fraction of a percent. It drifts as rates rise: at 25% it is off by several percent.
Why 72 rather than 69.3?
Because 72 divides evenly by 2, 3, 4, 6, 8, 9 and 12, which matters when the whole point is mental arithmetic. It also happens to compensate for the curvature at ordinary rates.
Does it work for inflation too?
Yes — for any constant compounding rate. At 3% inflation, prices double in about 24 years, which is the same arithmetic pointed at purchasing power.
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