Rule of 72 Calculator
↻ Updated 2026Enter an annual return to estimate how many years it takes to double your money, using both the Rule of 72 and the exact formula.
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How to read the Rule of 72 against the exact answer
At the default 8%, the Rule of 72 says 9.0 years and the exact formula says 9.01 — an error of four days. That's not luck. The rule was chosen to be near-perfect right around 8%, and the further you drag the slider from there, the worse it gets: at 20% it's off by 0.20 years, at 1% by 2.34.
Why dividing 72 by your return estimates doubling time
The exact question — how long until a balance doubles at rate r — has an exact answer: ln(2) ÷ ln(1 + r). The Rule of 72 is a mental shortcut for it, and where the 72 comes from tells you when to trust it.
ln(2) is 0.6931, so the exact formula is roughly 0.6931 ÷ ln(1 + r). For small rates ln(1 + r) is approximately r, giving 69.31 ÷ r% — the 'Rule of 69.3', accurate only for continuous compounding. Annual compounding needs the approximation nudged upward, and 72 is the nudge: it corrects the error into the range humans actually invest at, and it has more clean divisors than 69, 70 or 71.
Rule of 72: years ≈ 72 ÷ return% Exact: years = ln(2) ÷ ln(1 + return) where return is a decimal (8% → 0.08) error = (72 ÷ return%) − exact at 8%: 72 ÷ 8 = 9.00 years ln(2) ÷ ln(1.08) = 9.01 years
- return%
- The annual return, entered as a whole number — 8 for 8% — the rule divides by the number, not the decimal, which is the only reason 72 rather than 0.72
- return
- The same rate as a decimal, for the exact formula — 8% → 0.08; ln(1.08) = 0.0770
- ln(2)
- The natural log of 2 — the constant at the heart of any doubling — 0.6931; this is where 69.3 comes from, and 72 is its practical adjustment
- exact
- The true doubling time under annual compounding — 9.01 years at 8%; the number the rule is approximating
- error
- Rule of 72 minus exact, in years — positive means the rule is pessimistic (says it takes longer than it does)
The rule's accuracy is a curve with one crossing point, and the calculator's error field makes it visible. Below roughly 7.85% the rule overshoots — at 2% it says 36 years against a true 35, an error of a full year. Above the crossing it undershoots: at 12% it says 6.00 against 6.12, and at 20% it says 3.60 against 3.80. The signed error passes through zero somewhere between 7.8% and 7.9%, which is why the default of 8% shows an error of just −0.01 years.
In relative terms the rule holds up better than the raw years suggest, which is what makes it useful. It's within 1% of the truth across roughly 6-10% — the band that covers most long-run equity assumptions — and drifts to about 3% error at 1% or 15%, and 5% at 20%. That's why the rule survives despite being wrong everywhere: it's precise exactly where investors need it and sloppy where nobody's compounding anyway. For the real number rather than the estimate, the compound interest calculator compounds the balance directly.
Worked examples
Example: 8% a year — where the rule is nearly perfect
The calculator's default, and not an arbitrary one. 8% is roughly where the Rule of 72's approximation error crosses zero.
| Rule of 7272 ÷ 8 | 9.00 yr |
| Exact formulaln(2) ÷ ln(1.08) | 9.01 yr |
| Errorabout four days across nine years | −0.01 yr |
| Relative error | 0.07% |
| Rule of 69.3 for comparisonthe continuous-compounding version — worse here, off by 0.35 | 8.66 yr |
Four days out over nine years. This is the rule at its best, and it's the reason 72 was chosen over the mathematically purer 69.3: for annual compounding at the rates people actually plan around, 72 is simply more accurate. The exact formula's extra precision buys you nothing you can act on.
Example: the rate table, where the error grows in both directions
The doubling-time table on the page runs 2% to 12%. Reading it as a set shows the approximation's shape — the error is smallest in the middle and grows toward both ends, changing sign on the way.
| 2%rule is 1.00 yr pessimistic | 36.0 yr (exact 35.0) |
| 4%+0.33 yr | 18.0 yr (exact 17.7) |
| 6%+0.10 yr | 12.0 yr (exact 11.9) |
| 8%−0.01 yr — the crossover | 9.0 yr (exact 9.0) |
| 10%−0.07 yr, now optimistic | 7.2 yr (exact 7.3) |
| 12%−0.12 yr | 6.0 yr (exact 6.1) |
| 20%−0.20 yr — 5% relative error | 3.6 yr (exact 3.8) |
The error is 1.00 years at 2% and −0.20 at 20%, passing through zero near 7.85%. Notice the asymmetry: the rule is far worse at low rates in absolute terms, because the doubling time itself is enormous there and a small proportional slip is many years. If you're using this on a savings account paying 2%, the rule tells you 36 years when it's really 35 — an error longer than most people's patience.
Frequently asked questions
How accurate is the Rule of 72?
Very accurate in the band that matters, unreliable outside it. Across roughly 6-10% returns the rule lands within about 1% of the exact answer — at 8% the gap is four days over nine years. At 20% the relative error grows to about 5% (3.60 years against a true 3.80); at 1% it's 3.4% out, an absolute error of 2.34 years.
The rule overestimates doubling time below roughly 7.85% and underestimates above it, crossing over near the default of 8% — by construction, not coincidence. For a mental estimate about a portfolio the error is irrelevant. At an extreme rate, use ln(2) ÷ ln(1 + r), which this page shows next to it.
Why 72 and not 70 or 69?
Because 72 has more divisors than any nearby number, and the rule's entire value is being doable in your head. It divides evenly by 2, 3, 4, 6, 8, 9 and 12. 69 divides cleanly only by 3 and 23, which makes it useless as a mental shortcut regardless of its accuracy.
The mathematically 'correct' constant is 69.3 — ln(2) × 100 — and it's exact for continuous compounding. But most investments compound annually or monthly, and for annual compounding 69.3 is noticeably too low: 8.66 years at 8% against a true 9.01. So 72 is both easier to divide and more accurate for the common case — a rare instance of the convenient answer also being the better one.
How long does it take to double your money?
Divide 72 by your annual return. At 8%, nine years. At the S&P 500's roughly 10% long-run nominal average, 7.2 years — or about 10 years using its ~7% real return, which is the more honest figure since it doubles your purchasing power rather than your dollar count.
The rates make the point better than the arithmetic. A savings account at 0.5% doubles in 144 years. At 2%, 36 years. At 8%, nine. At 12%, six. Doubling time is the reciprocal of the rate, not a linear function of it — which is why the gap between 2% and 4% (18 years saved) dwarfs the gap between 10% and 12% (1.2 years). The first percentage points are worth far more than the last.
Does the Rule of 72 work for inflation and debt?
Yes — it's indifferent to what's compounding or which direction it helps. At 3% inflation, prices double in about 24 years (72 ÷ 3) and purchasing power halves on the same schedule; the exact answer is 23.4 years, so the rule is a little pessimistic there, as it is at all low rates.
It works on debt with the same brutality. A credit card at 24% APR doubles a balance you never pay in about three years. And it works on fees: a 1% annual expense ratio doesn't double anything, but the same reciprocal thinking applies — any constant rate compounding against a balance obeys this arithmetic. See the credit card payoff calculator for what that does to a real balance.
Should I use 72 with a nominal or a real return?
Whichever question you're asking, but know which one you answered. Using a nominal 10% gives 7.2 years to double your dollars. Using a real 7% gives 10.3 years to double what those dollars buy — and only the second is a doubling you'd notice in your life.
This is the rule's quietest trap. Doubling your money in 7.2 years sounds transformative; doubling it in 7.2 years while prices rise 24% over the same stretch is a more modest event. If you want the answer in purchasing power, subtract inflation from your return first — or, more precisely, use (1 + nominal) ÷ (1 + inflation) − 1 — and then divide 72 by that.
Where the Rule of 72 breaks down
It's an approximation of an approximation: a shortcut to a formula that itself assumes a world nothing invests in.
- It degrades at the extremes — Within 6-10% the error is under 1%. At 20% it's about 5% (3.60 years against 3.80), and at 1% it's 2.34 years off. A common fix is adjusting the numerator by one for every three points away from 8% — using 71 at 5%, or 74 at 14% — which restores most of the accuracy and destroys most of the convenience.
- Constant returns, and no contributions — The rule assumes one lump growing at a fixed rate with nothing added. A portfolio you're contributing to doubles far sooner than 72 ÷ r suggests, because you're adding money as well as earning it — the rule will be wildly pessimistic and it won't tell you.
- Compounding frequency — 72 is tuned for annual compounding. For continuous compounding the right constant is 69.3, which at 8% gives 8.66 years against 72's 9.00. The gap is small but it's in the opposite direction from the rule's usual error at that rate.
- No tax, no fees, no inflation — Doubling a taxable balance takes longer than the rule says, because tax comes out along the way. An 8% return in a taxable account at a 22% rate is really 6.24%, which doubles in 11.5 years rather than 9. The rule is only as honest as the rate you feed it.
- Real markets don't produce a rate — The formula needs a single constant number. Markets deliver a sequence — and a portfolio averaging 8% with volatility doubles later than a steady 8%, because variance drags compound growth below the arithmetic mean.
- ·Rule of 72 approximation
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