The Rule of 72 is a mental-math shortcut for a question that actually needs a logarithm to answer exactly: at a given growth rate, how long until money doubles?
How it works
Divide 72 by the annual growth rate. At 8% growth, money roughly doubles in 72 ÷ 8 = 9 years. The exact answer uses a natural logarithm — ln(2) ÷ ln(1 + rate) — which this calculator shows alongside the estimate.
Why 72, and not the exact number
The mathematically precise constant is 100 × ln(2) ≈ 69.3, not 72. 72 is used instead because it divides evenly by far more of the growth rates people actually ask about — 6, 8, 9, 12 — making it genuinely usable in your head, at the cost of a little accuracy that widens at lower growth rates.
How to use this calculator
- Enter the annual growth rate you expect.
- Compare the quick Rule of 72 estimate against the exact figure.
Frequently asked questions
Does the Rule of 72 work for any growth rate?
It stays reasonably close for the typical range of investment returns (roughly 4–15%); at very high or very low rates the gap to the exact figure widens noticeably.
Can I use this for inflation instead of investment growth?
Yes — the same math estimates how long until prices double at a given inflation rate, or equivalently, how long until purchasing power halves.
Is there a “Rule of 70” too?
Yes, some use 70 instead of 72 for the same reason — a slightly different trade-off between divisibility and precision. Both are approximations of the same 100×ln(2) constant.
Why does the gap between the estimate and the exact figure grow at low rates?
The Rule of 72 is a linear approximation to a curve (the logarithm) that bends away from a straight line more sharply at the low end.
