Rule of 72 Calculator
One rate in, and the years for your money to double — the mental-maths classic.
How this is calculated
years to double ≈ 72 ÷ rate; triple ≈ 114 ÷ rate; quadruple ≈ 144 ÷ rate
Worked example: at 8%, money doubles in about 9 years, triples in about 14, quadruples in about 18. It’s the quickest way to feel why a couple of extra percent, compounded, changes everything.
Why 72, and how good the approximation is
Dividing 72 by an annual growth rate gives the approximate years to double. It works because the exact answer is ln(2) ÷ ln(1+r), and ln(2) is about 0.693; using 69.3 would be more accurate at very low rates, but 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which is what makes it usable in your head. The approximation is closest around 8%, drifts under a percent at ordinary rates, and degrades above roughly 20%.
The variants exist for the same reason: 69.3 for continuous compounding, and 70 for a middle ground, which is why demographers use "rule of 70" for population growth.
It cuts both ways
The rule is as useful for costs as for gains. Inflation at 6% halves purchasing power in about twelve years. A 2% annual fund fee, compounded across a working life, consumes a startling share of a portfolio for exactly the same reason. Debt at 18% doubles in four years if left unpaid. Any compounding quantity — subscribers, cases, salary, damage — obeys it.
Where it misleads
It assumes a constant rate, which almost nothing has. Applied to an investment averaging 8% with high volatility, it describes a smooth path that will not be travelled, and the sequence of returns matters for anyone withdrawing. It also encourages the mistake of thinking about nominal doubling: money that doubles in nine years at 8% while inflation runs at 6% has barely gained in real terms. Subtract inflation from the rate before dividing, and the answer becomes far less exciting and far more honest.
Frequently asked questions
How accurate is the rule of 72?
Remarkably close for the rates most people deal with (roughly 4–15%). Dividing 72 by the annual rate gives the doubling time within a few months of the exact figure — a brilliant piece of mental arithmetic for judging investments on the fly.
Where does 72 come from?
It’s a rounding of the exact maths (ln 2 ÷ ln(1+r)) chosen because 72 divides cleanly by many rates — 2, 3, 4, 6, 8, 9, 12. The cousins 114 (triple) and 144 (quadruple) work the same way.