Rule of 72 Calculator — doubling time, estimated and exact

How it works

Two answers to one question. The shortcut, as the SEC's investor bulletin puts it: simply divide the number 72 by your investment's expected rate of return — 9% doubles about every 8 years. The exact answer solves (1+r)ᵗ = 2 for t, giving t = ln 2 ÷ ln(1+r). The rule works because ln 2 ≈ 0.693 and, for small rates, ln(1+r) ≈ r — so the true numerator is nearer 69.3, and 72's extra margin happens to compensate for the approximation error right where common rates live. The table runs both formulas from 2% to 12%: the gap is a few weeks around 9%, about a third of a year at 4%, and a full year at 2% — the honest boundary of a mental-math rule, visible in actual years.

Worked example

Both anchors are the regulators' own resolved cases. The SEC's: at an expected return of 9%, your investment doubles about every 8 years — 72 ÷ 9 = 8, this page's default, where the exact formula gives 8.04. FINRA's: money earning 4% doubles in 18 years — 72 ÷ 4 = 18, the preset, against an exact 17.7. The doubled-amount output keeps it concrete: $10,000 becoming $20,000 on that clock.

Frequently asked questions

What is the Rule of 72?

A mental-arithmetic estimate of doubling time: 72 divided by the annual rate in percent gives roughly the years for compounding money to double — the SEC's example is 9% doubling about every 8 years. It is an estimate by design; the exact output beside it shows how close it lands.

Why 72 and not some other number?

The exact doubling math uses ln 2 ≈ 69.3, so 69 or 70 would be truer for continuous compounding — but 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12, and its slight overshoot offsets the approximation error at ordinary annual rates. Convenience and accuracy meet in the middle.

How accurate is the rule?

Tightest near 9%, where the gap is a few weeks; about a third of a year at 4%; and roughly a full year of overshoot at 2%. At high rates it drifts the other way, undershooting slightly — the sweep makes both drifts visible in actual years for the range you care about.

Does the rule work for anything besides investments?

Any steady compounding process: inflation eroding purchasing power (3% inflation halves real value in roughly 24 years), debt growing at a card's rate, or a country's economy at a growth rate. Divide 72 by the annual percentage and the doubling — or halving — clock appears.

Can it estimate the rate instead of the years?

Yes — the same division backwards: 72 divided by the years to double gives the rate in percent. Wanting money doubled in 6 years implies needing about 12% a year, which the exact formula puts at 12.2% — the shortcut works both directions.

What does doubling actually require in practice?

A constant compounded return for the full period, reinvested — no withdrawals, fees, or taxes along the way. Real returns vary year to year, so the clock is an average-rate abstraction: useful for scale, not a schedule.

How accurate is this page, and what does it exclude?

The estimate is the published rule applied exactly; the exact figure is the closed-form doubling time for annual compounding. It excludes volatility, fees, and taxes, and it assumes annual compounding — other frequencies shift the exact answer slightly, which is the compound-interest calculator's territory.