Investing

Rule of 72 Calculator

The Rule of 72 is investing's handiest shortcut: divide 72 by your annual return to estimate the years it takes money to double. Enter a rate to see that estimate next to the exact figure — and how long a quadruple takes.

Formula shown below · Tested against worked examplesHow we verify

Annual return

Long-run stock returns have averaged ~10% nominal; use a lower real rate to plan in today's dollars.

Years to double (exact)

9.01

Using compound growth: ln 2 ÷ ln(1 + rate).

Rule of 72 estimate: 9
Years to triple: 14.27
Years to quadruple: 18.01

Compare scenariosTry three values of one input

Vary

Rule of 72 Calculator results for three values of Annual return
Annual return
Years to double (exact)	9.97	9.01−0.96	8.22−1.75
Rule of 72 estimate	10	9−1	8.18−1.82
Years to triple	15.8	14.27−1.53	13.03−2.77
Years to quadruple	19.94	18.01−1.93	16.44−3.5

Every other input stays at the value you set above — currently 8% for annual return. Differences are measured against the first column.

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How this calculator works

Exact years to double = ln(2) ÷ ln(1 + rate). The Rule of 72 estimate is 72 ÷ (rate as a percent). Tripling uses ln(3), and quadrupling is exactly twice the doubling time (two successive doublings).

This assumes a constant annual return compounded yearly. Real returns vary year to year, so treat the result as a planning estimate, not a guarantee — and use a real (after-inflation) rate to think in today's dollars.

Formula

Years to double ≈ 72 ÷ rate%

Exact: t = ln(2) ÷ ln(1 + r)

rate%: Annual return expressed as a whole number, e.g. 7 for 7%
r: The same rate as a decimal, e.g. 0.07
t: Years for the money to double

The shortcut is accurate to within a rounding error between roughly 5% and 12%: at 7% it gives 10.3 against a true 10.24. It drifts at the extremes — at 3% it says 24 where the answer is 23.4. It works on inflation too, which is its most useful application.

What this assumes

An approximation, most accurate between roughly 5% and 12%. It drifts at the extremes.
It assumes a constant rate with no contributions or withdrawals.
It answers doubling time only; it says nothing about the path or the risk.

What changes this number

The rate: Inversely proportional: doubling the rate roughly halves the time.
Accuracy band: At 3% it says 24 years against a true 23.4; at 12%, 6 against 6.1.
Applying it to inflation: The most useful version. At 3%, prices double in 24 years.

A worked example

Take the 8% stock-like return scenario. These figures are produced by the calculator above, not written alongside it, so they always match what the tool returns.

What you enter

Annual return: 8%

What it returns

Years to double (exact): 9.01
Rule of 72 estimate: 9
Years to triple: 14.27
Years to quadruple: 18.01

Sources

This calculator uses no external data — the result follows entirely from the formula above and the values you enter, so there is nothing to cite beyond the arithmetic.

Calculator last reviewed August 8, 2026. How we verify

Try an example

8% stock-like return Conservative 5%Inflation at 6%

Frequently asked questions

What is the Rule of 72?

The Rule of 72 estimates how many years it takes an investment to double: divide 72 by the annual percentage return. At 8% a year, 72 ÷ 8 = 9 years to double. It's a mental-math shortcut that's remarkably close to the exact compound-growth answer for the rates most investors see.

How accurate is the Rule of 72?

Very close for typical returns of about 6–10%, usually within a tenth of a year of the exact figure. It drifts a little at extremes — for very high rates the true doubling time is slightly longer than 72 suggests. For quick estimates it's more than good enough; this calculator shows the exact number beside it.

Why 72 and not another number?

The exact doubling time is ln(2) ÷ ln(1 + rate), and ln(2) ≈ 0.693, so multiplying by 100 gives about 69.3. But 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12, making the mental math easy — a small accuracy trade for a big convenience. Some people use 70 for continuous compounding.

Does the Rule of 72 work for inflation and debt?

Yes — the same math applies to anything compounding. At 6% inflation, prices double in about 12 years (72 ÷ 6), halving your money's purchasing power. On a 24% credit card, the balance can double in about 3 years if you don't pay it down. Compounding cuts both ways.