Rule of 72 Calculator
Estimate how long money takes to double at a given return using the Rule of 72, or the rate needed to double in a set time, with the exact figure for comparison.
Cómo usar esta calculadora
- 1Choose whether you know the rate and want the doubling time, or vice versa.
- 2Enter the annual rate of return, or the number of years available.
- 3Read the Rule of 72 estimate and the exact answer beside it.
- 4Use it to gauge how compounding and inflation reshape money over time.
Cómo funciona
Rule of 72
years to double ≈ 72 ÷ annual rate (%) rate to double ≈ 72 ÷ years exact years = ln 2 ÷ ln(1 + rate) the mathematically 'true' constant is ≈ 69.3
The Rule of 72 is a shortcut for estimating how long a sum takes to double under compound growth. Divide 72 by the annual percentage rate of return and the result is roughly the number of years to double; rearranged, dividing 72 by the number of years gives the rate needed to double in that time. The exact doubling time comes from logarithms — the natural log of 2 divided by the natural log of one plus the rate — but that requires a calculator, whereas 72 divided by a rate can be done in your head. The number 72 is a practical compromise: the mathematically exact constant is about 69.3, but 72 has far more whole-number divisors, making the mental arithmetic clean for the rates people most often use.
Ejemplo resuelto
At an 8% annual return, money doubles in about 72 ÷ 8 = 9 years, close to the exact figure of 9.01. In 18 years it would double twice, quadrupling. Turned around: to double your money in 6 years you need roughly 72 ÷ 6 = 12% a year.
Rule of 72 Calculator: la guía completa
A shortcut for grasping compound growth
Compound growth is famously hard to intuit — our minds expect straight lines, but compounding curves upward, and small differences in rate produce vastly different outcomes over time. The Rule of 72 is a wonderfully simple tool for building that intuition. By turning any rate of return into a doubling time you can compute in your head, it makes the abstract power of compounding concrete: at 8% your money doubles roughly every nine years, so over a 36-year career it doubles four times, becoming sixteen times its starting value.
This framing reveals things a raw percentage hides. The difference between a 6% and a 9% return sounds modest, but the Rule of 72 shows it as the difference between doubling every 12 years and every 8 — a gap that compounds into an enormous divergence over decades. It is precisely because the rule is so quick that it is useful: you can sanity-check an investment claim, compare options, or grasp the long-run stakes of a fee or a rate difference without reaching for a spreadsheet.
Why 72, and how accurate it is
The mathematically exact doubling time uses natural logarithms, and for continuous compounding the magic constant would be about 69.3 (which is 100 times the natural log of 2). So why does the rule use 72? Because 72 is far more convenient: it divides evenly by 2, 3, 4, 6, 8, 9, and 12 — most of the rates people actually care about — giving clean whole-number answers in your head, where 69.3 would give awkward decimals. The small inaccuracy this introduces is a worthwhile trade for the mental ease.
The rule is most accurate for rates in the middle of the common range, roughly 6% to 10%, where it lands within a fraction of a year of the true value. At very high rates it slightly overestimates the doubling time, and at very low rates it slightly underestimates it, which is why some people use 70 for lower rates or 69.3 when precision matters. For everyday financial reasoning, though, the standard 72 is close enough that the error is rarely material, and the calculator shows the exact figure alongside so you can see just how small the gap is.
Doubling, inflation, and the dark side of compounding
The Rule of 72 works in both directions, and its most sobering use is on inflation and debt rather than investment gains. Just as returns compound your wealth, inflation compounds the erosion of your money's value. At 3% inflation, prices double — and your cash halves in buying power — in about 24 years. At 6%, that falls to just 12 years. Applying the rule to an inflation rate is a quick, jarring way to see why leaving large sums in cash is not as safe as it feels.
The same logic exposes the danger of high-interest debt. A credit card charging 18% doubles the balance in about four years if left unpaid, which is why revolving debt spirals so quickly. The rule turns an abstract interest rate into a visceral timeline: the money you owe is doubling on a schedule you can calculate in seconds. Used this way, the Rule of 72 is not just an investing tool but a general lens for any compounding process — growth or decay — that helps you feel, not just calculate, how time and rate combine.
Preguntas frecuentes
What is the Rule of 72?
A mental-math shortcut for compound growth: divide 72 by the annual percentage return to estimate the years for money to double. At 8%, that's 72 ÷ 8 = 9 years. Rearranged, 72 divided by the years gives the rate needed to double in that time.
Why is it 72 and not 69?
The mathematically exact constant is about 69.3, but 72 divides evenly by many common rates — 2, 3, 4, 6, 8, 9, 12 — giving clean whole-number answers you can compute in your head. The tiny loss of accuracy is worth the mental convenience.
How accurate is the Rule of 72?
Very accurate for rates around 6–10%, landing within a fraction of a year of the exact value. It slightly overestimates at high rates and underestimates at low ones. For low rates, some use 70 or 69.3 instead. For everyday estimates, the error is rarely significant.
Can the Rule of 72 be used for inflation?
Yes — it estimates how fast inflation halves your money's buying power. At 3% inflation, prices double and cash halves in about 24 years; at 6%, in 12. It works for any compounding process, including high-interest debt, which at 18% doubles in about four years.