Rule of 72 calculator

Divide 72 by your rate to estimate the years it takes money to double. This one shows the estimate next to the exact answer, so you can see where the shortcut drifts.

How the math works

The Rule of 72 is one division. Take 72, divide by the annual rate written as a whole number, and you get the rough number of years for a sum to double.

The exact version comes from the compound-growth equation. A sum doubles when (1 + rate)t = 2, and solving for t gives ln(2) / ln(1 + rate). The Rule of 72 is a shortcut for that logarithm — 72 stands in for the messy natural-log math, and it works because 72 has clean divisors (2, 3, 4, 6, 8, 9, 12) that make the mental arithmetic easy.

The number that would make the shortcut exact isn't fixed at 72. It sits near 72 around an 8% rate, drifts down toward 69.3 — which is 100 × ln(2) — for very small rates, and climbs above 72 as the rate rises. That drift is the whole story of when the rule is safe to use.

Worked example

The S&P 500's long-run average annual nominal return is 10.2%. Plug it in: 72 / 10.2 is about 7.06 years to double. The exact figure is 7.14 years. The shortcut lands within about a month of the truth, which is why the rule is a fine back-of-envelope tool for stock-market rates.

Now switch to the real return — after inflation — which has averaged 7.0%. The rule says 72 / 7, or about 10.3 years. The exact answer is 10.24 years. Same shortcut, still close, but notice the error flipped sign: at 10.2% the rule guessed a touch too fast, and at 7.0% it guessed a touch too slow. That sign flip is the part most calculators skip.

When this calculator is wrong

The rule is a shortcut, and shortcuts have a shape to their error. Knowing that shape is the difference between using it well and trusting it blindly.

• It only works on a single lump sum. The Rule of 72 assumes one amount compounding on itself with nothing added. Apply it to a 401(k) or any account you keep contributing to and the answer is meaningless — the ongoing deposits, not compounding alone, do most of the early lifting. For that, you want a compound interest calculator, not this one.
• Below about 8%, the rule overstates the time; above it, the rule understates it. At a 4% rate the rule says 18 years to double when the truth is closer to 17.673. At high rates it drifts the other way and faster. A balance at the U.S. average credit card APR of 22.76% doubles in about 3.38 years, but the rule's 72 / 22.76 says 3.16 — it undersells how long the debt actually takes to compound, which cuts the wrong way when the number you care about is how fast you owe double.
• The correction is to move the numerator, not to abandon the rule. A common field adjustment: nudge the numerator by 1 for every 3 percentage points the rate strays from 8% — roughly 71 at 5%, 73 at 11%. For continuously compounded rates, use 69.3 instead of 72.
• It says nothing about whether the rate holds. Doubling in 7 years assumes the rate never moves. A savings account at the FDIC national average of 0.41% would, on paper, take over 170 years to double — a number the rule will happily compute and that tells you only that cash at that rate never really doubles at all.

What to do with the result

Use the rule for the thing it is good at: a fast gut-check on whether a rate is worth caring about. If a pitch promises to double your money in five years, the rule back-solves the required return in one step — 72 / 5 is about 14% a year, well above what a diversified portfolio has returned, which tells you to read the fine print.

For any decision with real dollars attached — a retirement projection, a debt payoff plan, an account you contribute to monthly — drop the shortcut and run the full compound math. The rule is a compass, not a map. It points you at the right order of magnitude; it does not survive contact with a spreadsheet.

Common questions

Why 72 and not 70 or 69?

The mathematically exact constant for continuous compounding is 69.3 (that's 100 × ln 2). But 72 has far more clean divisors — 2, 3, 4, 6, 8, 9, 12 — which makes the mental math easy, and it happens to be most accurate right around the 8% rate that real portfolios often earn. It's a trade of a little precision for a lot of convenience.

Is the Rule of 72 accurate?

For annual rates between 6% and 10% it lands within about 1% of the exact doubling time. Outside that band it drifts: it overstates the time below roughly 8% and understates it above, and the error grows as the rate moves further from that range.

Can I use it for my 401(k) or monthly investing?

No. The rule assumes a lump sum with no further contributions. An account you add to every month grows on both compounding and new deposits, and the rule ignores the second half. Use a compound interest calculator with a contribution field instead.

How do I use it to find a required rate of return?

Divide 72 by the number of years instead. To double in 10 years you need about 72 / 10, or 7.2% a year; the exact figure is 7.18%. The "Rate to double?" mode above does this for you.

Does the rule work for tripling money?

Not directly — 72 is calibrated to doubling. For tripling, the analogous shortcut divides about 114 by the rate; for quadrupling (two doublings) you simply double the Rule of 72 answer.