Calculate how long it takes to double your money. Rule of 72 estimate plus exact formula, with growth chart and common-rate comparison.
A free Rule of 72 calculator that instantly tells you how many years it takes for your investment to double at any annual return. Compare the classic 72÷rate% shortcut against the exact mathematical formula ln(2)/ln(1+r), see required rates to hit a doubling target, calculate money multipliers over any horizon, and visualise the doubling points on an animated growth chart. Includes side-by-side common-rate comparisons (savings, bonds, stocks, aggressive, crypto) in USD, INR or AED.
The Rule of 72 derives from the compound-interest equation FV = PV·(1+r)^t. Solving for t when FV = 2·PV gives t = ln(2)/ln(1+r). Since ln(2) ≈ 0.6931, and for small r the denominator ln(1+r) ≈ r, the doubling time approximates to 0.6931/r — about 69.3 when r is expressed as a percentage. The number 72 was adopted as a practical substitute because it factors cleanly: 72÷2, ÷3, ÷4, ÷6, ÷8, ÷9, ÷12 all yield clean integers. The trade-off is a tiny accuracy loss in exchange for memorability.
Compound interest is famously (if perhaps apocryphally) attributed to Albert Einstein as "the eighth wonder of the world. He who understands it, earns it; he who does not, pays it." The Rule of 72 is the simplest tool for grasping just how powerful compounding is over decades. A 25-year-old investing at 10% per year sees their money double roughly every 7.2 years — that is five doublings (32×) by retirement at 65, all from a single deposit. Doubling time is the lever that turns time into wealth.
The Rule of 72 assumes a constant, positive rate of return — a luxury real markets rarely provide. Stock returns are volatile: an "average" 10% can mask 20% gains and 30% drawdowns, and sequence-of-returns risk means the same average produces different doubling times depending on the order. Inflation erodes the real doubling time (use real returns, not nominal). Taxes and fees compound against you — a 1% management fee on a 7% return turns a 10.3-year doubling into a 12-year doubling. Always pair the Rule of 72 with realistic, after-fee, after-tax, after-inflation rate assumptions.
The Rule of 72 is a mental-math shortcut for estimating how long it takes money to double at a fixed compound rate. Divide 72 by the annual return percentage — the answer is the doubling time in years. At 8%, money doubles in ~9 years (72÷8).
Both are approximations of ln(2)/ln(1+r). Rule of 70 is more accurate for low rates (under 6%) and continuous compounding. Rule of 72 is preferred because 72 has more divisors (2,3,4,6,8,9,12) which makes mental math easier, and it is most accurate at 6–10% returns.
Within about 1% of the exact answer for rates between 6% and 10%. Above 15% or below 4% the error grows — at 25% the Rule of 72 says 2.88 years but the exact answer is 3.11 years. This calculator shows both side by side.
Setting (1+r)^t = 2 and taking logs gives t = ln(2)/ln(1+r). For small r, ln(1+r) ≈ r, so t ≈ ln(2)/r ≈ 0.693/r. Multiplied by 100 that is ~69.3/rate%, but 72 is used because it divides cleanly by more whole numbers.
The rule assumes a fixed positive return, no withdrawals, no taxes, and steady compounding. It is unreliable for volatile assets (where actual returns whip around the average), high inflation environments, or after-fee returns. Use it as a back-of-envelope reality check, not a forecast.
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