Rule of 72 Calculator

Estimate investment doubling cycles or determine required yields using the shorthand Rule of 72.

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Awaiting Parameters

Provide your parameters to run doubling projections.

Rule of 72 Comparison Matrix

Rule of 72 estimate vs. exact logarithmic doubling time

Annual Rate Rule of 72 (Yrs) Exact Time (Yrs) Difference
1%72.0 yrs69.7 yrs +2.3 yrs
2%36.0 yrs35.0 yrs +1.0 yrs
3%24.0 yrs23.4 yrs +0.6 yrs
4%18.0 yrs17.7 yrs +0.3 yrs
5%14.4 yrs14.2 yrs +0.2 yrs
6%12.0 yrs11.9 yrs +0.1 yrs
7%Sweet Spot10.3 yrs10.2 yrs +0.1 yrs
8%Exact Match9.0 yrs9.0 yrs 0.0 yrs
10%7.2 yrs7.3 yrs −0.1 yrs
12%6.0 yrs6.1 yrs −0.1 yrs
15%4.8 yrs5.0 yrs −0.2 yrs
20%3.6 yrs3.8 yrs −0.2 yrs
Rule overestimates (positive diff) Exact match at 8% Rule underestimates (negative diff)

Rule of 72 vs Exact Formula

Where the mental shortcut holds, where it drifts, and what it means for debt, inflation, and real assets.

72 ÷ rate = years to double
8%
Years to double
9.0yrs
Rule of 72 vs. exact formula Approximation
Rule of 72, at 1%
72.0yrs
2.3 years off at low rates
VS
Exact formula, at 1%
69.7yrs
ln(2) / ln(1.01)
At 8%, both agree almost exactly — 9.0 vs 9.01 years. The gap only opens up at the extremes.
Rule of 72 vs. Rule of 70 vs. Rule of 69.3 Verified
Rate Rule of 72 Rule of 70 Rule of 69.3 Exact
1%72.070.069.369.66
2%36.035.034.6535.00
3%24.023.323.123.45
4%18.017.517.3317.67
6%12.011.711.5511.90
8%9.08.758.669.01
10%7.27.06.937.27
12%6.05.835.7756.12
15%4.84.674.624.96
25%2.882.82.773.11
Rule of 69.3 is mathematically exact (derived from ln(2) ≈ 0.693). Rule of 72 wins on usability — divisible by more whole numbers, so it's faster for mental math in the 4–18% range.
Sweet spot
4–18%

Inside this range, the Rule of 72 stays within a few weeks of the exact answer — close enough for any real-world planning decision.

Applied to debt and inflation Two-sided
Credit card debt at 22% APR
3.3yrs to double
A $5,000 balance becomes $10,000 in 3.3 years, and $20,000 in 6.6 years — if left untouched

At 3% inflation, prices double roughly every 24 years — a slow, steady erosion most people don't notice year to year.

At a peak 9.1% inflation, purchasing power halves in under 8 years — fast enough to reshape a household budget within a single decade.

ScenarioRateDoubles in
S&P 500 average10%7.2 years
Conservative portfolio5%14.4 years
Inflation, historical avg3%24 years
Credit card debt22%3.3 years
Payday loan400%0.18 years (10 weeks)
Historical doubling times for real assets Historical avg.
Asset classAvg. returnDoubling time
S&P 500 (total return)10.5%~6.9 years
US real estate8%~9 years
Gold7%~10.3 years
US Treasury bonds4.5%~16 years
High-yield savings (2024)5%~14.4 years
Savings account (pre-2022)0.5%~144 years
At 0.5% — what most major banks paid for a decade — your money takes 144 years to double. High-yield savings or diversified index investments are the difference between outpacing inflation and quietly losing to it.
Mental math drills Practice
Earning 4.8% in a high-yield savings account — how long to double $20,000?
15 years
A mortgage charges 6.75% — when does accrued interest match the original loan?
≈ 10.7 years
Inflation runs at 3.6% — when does a $200 grocery bill become $400?
20 years
A CD pays 5.4% over a 3-year term — does the balance double?
No — ~17% growth
A pitch promises 48% annual returns — how long to 8x (3 doublings)?
4.5 years*
National debt grows at 5% annually — when does it double?
14.4 years
*Only if the 48% rate holds — treat sustained returns at this level with skepticism.
Where the Rule of 72 breaks down Use with caution
RateRule of 72ExactErrorUse instead
20%3.60 yrs3.80 yrs-5.3%ln(2)/ln(1.2)
30%2.40 yrs2.64 yrs-9.1%Exact formula
50%1.44 yrs1.71 yrs-15.8%Exact formula
100%0.72 yrs1.00 yr-28.0%Exact formula
The exact formula is t = ln(2) / ln(1 + r), where r is the decimal rate. Above ~20%, switch to this log expression — the Rule of 72 systematically underestimates doubling time.