Rule of 72 Calculator

A doubling estimate you can run in your head

Divide 72 by the interest rate and the answer is roughly how many years until the money doubles. At 7%, money doubles in about 10.3 years. At 8%, 9 years. At 4%, 18 years. At 12%, 6 years. The rule is approximate, but across typical investment rates it lands within a fraction of a year, and it is fast enough to run mid-conversation. It appears in print as early as 1494, in Luca Pacioli's Summa de Arithmetica, more than a century before Napier published the logarithms in 1614 that supply the algebra behind it.

Why it works

The precise doubling time is ln(2) / ln(1 + r), where r is the decimal rate. For small rates that approximates to 0.693 / r, which is where the number 69.3 comes from. Two separate things recommend 72 over 69.3, and they are worth keeping apart. The first is arithmetic convenience: 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, so the division stays mental across the common rate range. The second is accuracy. Because the rule divides its constant by a rate written as a percentage, the constant that would make it exact is 100r × ln(2) / ln(1 + r), with r still the decimal rate. That quantity climbs steadily: 69.66 at 1%, 71.37 at 6%, 72.00 at 7.85% and 72.73 at 10%. Because it passes through 72 at about 7.85%, the rule overestimates doubling time below that rate and underestimates it above. At 6% it reads 12.00 years against a true 11.90; at 10% it reads 7.20 against 7.27. Between 6% and 10% the error stays under 1% of the true doubling time, and under 2% out to 12%. Beyond that band the approximation still works as a rough check, just less precisely.

Applied to common financial questions

The rule works directly on any compound growth or decay. Some applications:

How long until an investment doubles? At a 7% real return: 72/7 = 10.3 years.

How long until inflation halves the value of money? At 3% inflation: 72/3 = 24 years. At 5% inflation: 72/5 = 14.4 years.

How long until a credit card balance doubles if nothing is repaid? At 22% APR: 72/22 = 3.3 years. Repaying exactly the interest each month holds the balance flat instead, so doubling assumes no repayment at all.

What rate doubles money in 10 years? 72/10 = 7.2% a year.

What rate doubles a debt in 5 years? 72/5 = 14.4%.

Where the rule breaks down

The Rule of 72 assumes annual compounding and steady positive compound growth. It does not describe simple-interest products, where doubling takes 100/rate years: at 7% that is 14.3 years rather than 10.3. It also loses precision where returns vary enough that the average hides large swings, and at rates above about 19.2%, where the error passes 5%. Explicit calculation is more reliable in those cases.

The loss-recovery problem (a separate issue)

Loss recovery is often confused with the Rule of 72, but it is a different concept. Losing 50% requires gaining 100% to recover, not because the Rule of 72 breaks, but because percentages are asymmetric. A portfolio that drops from 10,000 to 5,000 has lost half its value. Bringing it back to 10,000 means doubling the remaining 5,000, which is a 100% gain. This asymmetry is why drawdowns hurt more than equivalent-percentage rallies help. Recovery scenarios need explicit compound-growth math; the Rule of 72 describes steady positive growth only.

The Rule of 114 (tripling) and Rule of 144 (quadrupling)

Less famous siblings that work the same way. 114 divided by the rate gives years to triple; 144 divided by the rate gives years to quadruple. At 7%, money triples in about 16.3 years and quadruples in about 20.6 years. The pattern behind the three numbers is that each is 72 scaled by how many doublings the multiple represents: 2x is one doubling, 3x is about 1.58 doublings (72 × 1.58 is close to 114), and 4x is exactly two (72 × 2 = 144). Two doublings already reach 4x, which is why 144 is simply twice 72.

The 70 variant and when it's better

Some financial resources use 70 instead of 72. Mathematically, 70 is closer to the true constant at low rates. The argument for 72 is easier mental math, since 72 divides more cleanly. The argument for 70 is marginally better accuracy at very low rates; the two swap places at about 4.9%, the rate at which the exact constant passes 71. At 2% inflation, 70/2 = 35 years, 72/2 = 36 years, and the true figure is 35.0 years. The difference is one year across a 35-year horizon, real but small. Either works for practical purposes. The cultural default in finance is 72; in economics, where lower rates matter more, 70 is sometimes preferred.

What an advertised return implies

Run backwards, the rule converts a headline into an implied annual rate. A pitch to double an investment in 4 years implies 72/4 = 18% a year. Doubling in 6 years implies 12%. Doubling in 10 years implies 7.2%. The arithmetic says nothing about whether any particular claim holds. It converts the promise into a rate, which can then be read alongside the risk the investment is described as carrying.

The compound debt implication

The same arithmetic runs on debt. By the rule, a balance at 29.9% doubles every 2.4 years, one at 22% every 3.3 years, and one at 35% every 2.1 years. All three rates sit above the band where the rule is precise, so it overstates how fast they compound: the exact doubling times are 2.65, 3.49 and 2.31 years. Under the rule, a 5,000 balance at 29.9% reaches roughly 20,000 in about 4.8 years with no repayments; the exact compound figure is 5.3 years. The mechanic that compounds savings compounds a balance the same way, which is what the rule makes visible in a way an APR percentage does not.

The one-rate limitation

The rule assumes a constant rate over the doubling period. Real investment returns vary year to year. A portfolio averaging 7% might return 15% some years and -10% others. The Rule of 72 still works here, but only on the compound average, not the arithmetic one. Fifteen percent followed by minus ten percent averages 2.5% arithmetically and 1.73% compounded, and the rule reads 28.8 years against the first and 41.5 years against the second, where the true answer is 40.3. The path to that average is also what makes the horizon hard to sit through. Knowing that 7% doubles in 10 years does not change what a 20% drop at year 2 feels like. The arithmetic is clean; the behaviour required to reach the doubling is the harder part.

What the calculator does

The tool applies the Rule of 72 to an interest or growth rate and returns the approximate doubling time, alongside the precise ln(2)/ln(1+r) figure for comparison. It is a mental-model trainer more than a precision instrument. For exact doubling-time requirements, the compound interest calculator solves for t directly. For quick checks and reality-testing claims, the rule is faster.