InvestmentCalculators

Rule of 72 Calculator

A quick mental-math trick for estimating how fast your money doubles at a given compound rate.

Solve for

7.0%
Rule of 72
10.3 years
Exact doubling time
10.2 years
Computed from compound interest formula

Rule of 72 vs. exact formula

Doubling time in years across common return rates — the rule is almost exact at 8%.

How this calculator works

The Rule of 72 is a well-known approximation: divide 72 by the annual rate expressed as a percent to get the approximate number of years to double. Conversely, dividing 72 by a target number of years gives the required annual rate.

The exact doubling time is ln(2) / ln(1 + rate), which is approximately 0.6931 / ln(1 + rate). The Rule of 72 is most accurate for rates between 5% and 10%. At 8% it's essentially exact; at higher rates it slightly under-estimates the required time and at lower rates it slightly over-estimates it. The calculator shows both approximations side by side so you can see the gap.

Why the Rule of 72 is useful

Despite the precise mathematical alternatives available on every phone, the Rule of 72 is genuinely useful. It lets you do compound interest mental math instantly: at 7%, money doubles roughly every 10 years. At 10%, roughly every 7. That intuition transforms how you think about investment horizons.

Most personal-finance decisions reward fast, approximate reasoning. Should you take a job at a 10% higher salary if it requires a move? Should you pay down a 5% mortgage faster or invest? Will a CD at 4% beat inflation over a decade? In each case, the Rule of 72 gives you the doubling-time ballpark — enough to frame the decision without a spreadsheet.

The rule has real mathematical justification. The exact doubling-time formula, ln(2) / ln(1 + r), Taylor-expands to approximately 69.3 / r for small r. We use 72 instead of 69.3 because 72 has more integer divisors (2, 3, 4, 6, 8, 9, 12, 18, 24, 36), making the mental arithmetic easy. For quick reasoning, that divisibility matters more than a percentage point of accuracy.

For rates well outside 4-12%, the rule's precision degrades. At 1% rates it significantly underestimates doubling time; at 20%+ it overestimates. For those edge cases, use the chart to read the exact number, or just fall back to a compound-interest calculator.

Frequently Asked Questions

How accurate is the Rule of 72?
Within ±5% of the exact answer for rates between roughly 4% and 12%. At 8% it's nearly exact. The larger the deviation from 8%, the larger the small error — but the rule remains useful for quick mental math throughout most real-world rates.
Why 72 and not 69 or 70?
The true mathematical constant is ln(2) × 100 ≈ 69.3. But 72 has more integer divisors (2, 3, 4, 6, 8, 9, 12, 18...), making mental division easier. The small loss in accuracy is worth the speed gain.
Can I use this for inflation or debt?
Yes. If inflation is 3%, prices double roughly every 24 years (72 / 3). If credit card debt compounds at 24%, the balance doubles every 3 years. The math works the same way for any compounding rate.
Does frequency of compounding matter?
The Rule of 72 assumes annual compounding. Monthly or daily compounding is slightly faster — for a 7% nominal rate, monthly compounding produces an effective annual yield of about 7.23%, which means doubling happens marginally sooner than the rule suggests. The difference is small at typical rates.
Are there other similar rules?
Yes. The Rule of 114 estimates tripling time (e.g., at 8%, money triples in about 114/8 = 14.25 years). The Rule of 144 estimates quadrupling time. For estimating halving (inflation erosion), the same Rule of 72 works in reverse: at 3% inflation, purchasing power halves in about 24 years.

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