Rule of 72 Calculator
A mental-math shortcut for how long an investment takes to double — and how close the shortcut really is to the exact answer.
Divide and done
Divide 72 by your rate and you have the doubling time in your head — no calculator needed.
An approximation
It is a handy estimate, most accurate around 8%, not an exact formula.
What is the Rule of 72?
The doubling-time shortcut
The Rule of 72 is a quick way to estimate how many years it takes for money to double at a fixed annual rate of return: just divide 72 by the rate. At 8% a year, money doubles in roughly 72 ÷ 8 = 9 years. As references such as Investopedia explain, it is a simplified stand-in for the exact logarithmic formula, accurate enough for mental math and especially close for rates in the 6–10% range. Sister rules — 114 for tripling and 144 for quadrupling — extend the same trick to larger growth targets.
The estimate divides a fixed rule number by the annual rate; the exact time uses logarithms.
Years ≈ 72 ÷ Rate (exact: ln 2 ÷ ln(1 + r))The rule number is 72 for doubling, 114 for tripling, and 144 for quadrupling — each chosen so that dividing by the rate (as a whole-number percent) lands close to the true logarithmic time. The exact doubling time is the natural log of the growth multiple divided by the natural log of one plus the periodic rate. The calculator shows both so you can see how good the shortcut is for the rate you entered.
You expect an 8% annual return and want to know how long your money takes to double.
Pick the rule number
Doubling uses 72.Divide by the rate
72 ÷ 8 = 9 years — the Rule of 72 estimate.Compare with exact
The precise figure is ln 2 ÷ ln 1.08 ≈ 9.01 years.Judge the shortcut
The estimate is off by less than a week — at 8% the rule is almost perfect.
72 is a convenient compromise: it has many whole-number divisors and sits near the true constant of about 69.3.
Best near 8%
The rule is most accurate for rates around 6–10%, where the estimate and exact answer nearly coincide.
High rates undershoot
At very high rates the rule slightly understates the doubling time, so the true wait is a little longer.
Low rates overshoot
At low rates it overstates the time; some people switch to 70 or 69.3 for more precision there.
The exact doubling constant is 100 × ln 2 ≈ 69.3, but 72 is preferred because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12, making the mental arithmetic effortless. The small inaccuracy this introduces is the price of a number you can actually divide in your head.
The estimated years is the Rule of N answer — the headline shortcut. The exact years is the true logarithmic figure, and the difference shows how far the approximation strays for your rate, positive when the rule overstates the wait and negative when it understates it. Use the estimate for quick comparisons — doubling in 9 years at 8% versus 12 years at 6% makes the power of a higher return tangible — and lean on the exact figure when precision matters. The rule is a teaching tool for the force of compounding, not a substitute for a full projection.
The Rule of 72 is a shortcut, with all the trade-offs that implies.
An estimate that assumes a steady rate
The rule assumes a single, constant rate of return compounded once per period and no deposits, withdrawals, taxes, or fees — none of which hold perfectly in real investing. Its accuracy fades at rates far from 8%, and it says nothing about the volatility or risk of actually earning that rate. Treat it as an informational rule of thumb for understanding compounding, and consult a qualified financial advisor before making investment decisions based on a projected doubling time.