Quick answer
The rule of 72 estimates doubling time: divide 72 by your annual return. At 8%, money doubles in about 9 years (the exact answer is 9.01 years). At 4%, it takes about 18 years. It also works in reverse for inflation and debt.
How the Rule of 72 Calculator works, step by step
Enter an annual rate of return. The calculator divides 72 by the rate and shows the approximate years to double, alongside the exact logarithmic answer and the percentage error, so you can see how close the shortcut lands. Enter a target number of years instead and it reverses the calculation: the return you need to double in that time, rule estimate and exact figure side by side.
The rule works because 72 is close to 100 × ln(2) adjusted for typical rates, and because 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12. It is most accurate between about 5% and 12%; at very low or very high rates the error grows, which the exact figure exposes. At 2% the rule gives 36 years against an exact 35.0; at 20% it gives 3.6 years against an exact 3.8.
The comparison table runs the rule against the exact answer at 2%, 4%, 6%, 8%, 10%, 12% and 15%, so you can see where the shortcut drifts. The error is smallest in the middle of that range and largest at the ends — which is fine, because the rates most savers actually meet sit in the middle, and the rule was built for mental arithmetic, not contracts.
Apply it beyond investments. At 3% inflation, purchasing power halves in about 24 years (the exact figure is 23.45). The same logic prices debt directly: a $5,000 card balance at 24% APR doubles to $10,000 in about 3 years if no payments are made — and the exact figure, 3.22 years, is close enough to the rule's 3.0 that the warning lands either way. The same three-second calculation frames all three decisions: growth, erosion and debt.
Know its limits. The rule describes a single sum compounding; with monthly contributions your balance doubles faster than the rule suggests because new money keeps arriving. Use it to judge the growth engine, and a savings or investment calculator for the contribution plan itself. For any figure that goes into a contract or a tax return, use the exact formula.
The formula
Years to double ≈ 72 ÷ annual rate (%). Exact: years = ln(2) ÷ ln(1 + r). Required rate to double in a target time ≈ 72 ÷ target years.
Worked example — try it on the calculator above
Worked example: doubling at 8%
72 ÷ 8 = 9 years. The exact calculation, ln(2) ÷ ln(1.08), gives 9.01 years — the rule is off by about four days. Invest $10,000 at a steady 8% and it becomes roughly $20,000 in year 9, $40,000 in year 18 and $80,000 in year 27: three doublings in total, which is why starting a decade earlier matters more than most contribution increases. At 4% the same three doublings take about 54 years instead of just 27.
Frequently Asked Questions
Why 72 and not 70 or 69?
69.3 is the mathematically exact constant for continuous compounding, and 70 is a common alternative. 72 is used because it divides evenly by most rates people actually meet and it slightly corrects for annual compounding at mid-range rates, landing closer than 69.3 does between 5% and 12%.
How accurate is the rule of 72?
Very close in its sweet spot: at 8% it gives 9 years against an exact 9.01. At 2% it gives 36 years against an exact 35.0 — about a year out. At 20% it gives 3.6 years against an exact 3.8. For planning estimates, the error is acceptable; for contracts, use the exact formula.
Can I use the rule for monthly contributions?
Not directly — the rule describes a single sum compounding. With monthly contributions your balance doubles faster than the rule suggests because new money keeps arriving. Use it to judge the growth engine, and a savings or investment calculator for the contribution plan itself.
What return makes money double in 10 years?
72 ÷ 10 = 7.2% a year (the exact figure is 7.18%). That is a useful benchmark: a portfolio returning about 7% doubles each decade, before inflation. Against 3% inflation, the real doubling takes roughly 17 years because the real return is about 4%.
Estimates, not advice. This calculator provides educational estimates based on the inputs you enter and the assumptions shown on this page. It is not financial, tax or investment advice, and it cannot see your full situation. Verify important figures against official sources, and consider a qualified professional for decisions about your own money. See our Disclaimer and Methodology.