Rule of 72 Calculator

Q: Is the Rule of 72 exact?

No — it's a close approximation. The exact formula is ln(2) ÷ ln(1 + r). For returns between roughly 4% and 15%, the rule of 72 is accurate to within a few percent.

The fastest mental shortcut in finance: how many years until your money doubles? Edit either number — the other updates instantly.

At a 7% annual return, your money doubles in about 10.3 years — that's the Rule of 72 (72 ÷ 7 ≈ 10.3). The rule is a quick mental shortcut: divide 72 by your expected annual return to estimate how many years it takes to double your money, or divide 72 by your target doubling time to find the return you need. It's most accurate for returns between about 5% and 12%. Edit either number below to explore the relationship instantly.

Your inputs

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Annual rate of return

…or years to double

Type in either field — the Rule of 72 links them: years × rate ≈ 72.

Money doubles in

~10.2 years

Rule of 72 estimate: 10.3 years

Rule of 72 estimate10.3 years

Exact (ln 2 ÷ ln(1+r))10.2 years

To double in 10 years, you'd need about 7.2% per year.

Annual return	Rule of 72	Exact
4%	18.0 years	17.7 years
5%	14.4 years	14.2 years
6%	12.0 years	11.9 years
7%	10.3 years	10.2 years
8%	9.0 years	9.0 years
10%	7.2 years	7.3 years
12%	6.0 years	6.1 years

How the Rule of 72 works

The rule

To estimate how long it takes money to double at a given annual return, divide 72 by the return (as a percentage):

Years to double ≈ 72 ÷ (annual return %)

Example: at 7% return, 72 ÷ 7 ≈ 10.3 years. Flipped the other way: to double in 10 years you need about 72 ÷ 10 = 7.2% per year.

The exact math

The rule is an approximation of the true formula, which comes from solving (1 + r)ⁿ = 2 for n:

n = ln(2) ÷ ln(1 + r)

where r is the annual return and n is the number of years. The Rule of 72 stays accurate to within a few percent for returns between roughly 4% and 15%.

View the formula →

Educational purposes only. Not financial advice. The rule assumes a constant return and ignores taxes, fees and volatility. See the methodology and disclaimer.

Worked examples

See how the Rule of 72 works in practice. The rule estimates how long it takes for your money to double at a given annual return.

Example 1: How fast does your money double?

Rule of 72 estimate vs. exact calculation · different annual returns

2% return

36.0y

exact: 35.0y

4% return

18.0y

exact: 17.7y

7% return

10.3y

exact: 10.2y

10% return

7.2y

exact: 7.3y

15% return

4.8y

exact: 5.0y

The Rule of 72 is remarkably accurate for typical investment returns (4–15%). At 7%, it estimates 10.3 years to double — the exact answer is 10.2 years, a difference of just 0.1 years. At the extremes (2% or 15%), it's slightly less accurate but still within 0.2–0.3 years. The rule works because 72 is conveniently divisible by many common rates (72 ÷ 6 = 12, 72 ÷ 8 = 9, 72 ÷ 9 = 8), making mental math easy. For a quick back-of-the-envelope estimate, it's hard to beat.

Example 2: The power of doubling — $10,000 over 30 years

Starting with $10,000 · no additional contributions · different annual returns

7% annual return

$76,123

doubles ~3 times in 30 years

10% annual return

$174,494

doubles ~4 times in 30 years

Here's why the Rule of 72 matters: at 7%, your money doubles roughly every 10.3 years. Over 30 years, that's about 3 doublings — $10,000 → $20,000 → $40,000 → $80,000 (the actual $76,123 is slightly less because 10.3 × 3 = 30.9 years, not exactly 30). At 10%, money doubles every 7.2 years — that's over 4 doublings in 30 years, turning $10,000 into $174,494. The difference between 7% and 10% isn't just 3 percentage points — it's double the final amount. This is why small differences in your annual return compound into enormous differences over long time horizons.

Example 3: Using the rule in reverse — what return do I need?

Want to double your money in a specific time? · rearrange the formula

Double in 10 years

7.2%

72 ÷ 10

Double in 7 years

10.3%

72 ÷ 7

Double in 5 years

14.4%

72 ÷ 5

The Rule of 72 works in reverse too: if you want to double your money in 10 years, you need a 7.2% annual return (72 ÷ 10). If you want to double in 7 years, you need 10.3%. If you want to double in just 5 years, you'd need 14.4% — a return that's very difficult to achieve consistently without taking significant risk. This reverse application is useful for setting realistic expectations: if someone promises you can "double your money in 3 years," that requires a 24% annual return — a red flag for fraud or extreme risk. The historical average for U.S. stocks is about 7–10% annually, which means doubling every 7–10 years is realistic, but much faster is not.

All examples use the Rule of 72 approximation and exact compound interest for comparison. Actual investment returns are not constant and will vary. See full disclaimer.

Rule of 72, explained

What is the Rule of 72?

A mental math shortcut: divide 72 by your annual return (as a percentage) to estimate how many years it takes your money to double. At 7%, for example, your money doubles in about 72 ÷ 7 ≈ 10.3 years.

Why 72 and not 70?

72 has lots of factors — 2, 3, 4, 6, 8, 9, 12 — so it divides cleanly for common rates like 6%, 8%, 9% and 12%. The number 69.3 (derived from the natural log of 2) is slightly more accurate across all rates, but 72 is much easier to do in your head.

Is the Rule of 72 exact?

No — it's a close approximation. The exact formula is ln(2) ÷ ln(1 + r). For returns between roughly 4% and 15%, the rule of 72 is accurate to within a few percent.

Does the Rule of 72 work for negative returns?

Roughly. With a negative rate it estimates how long your money takes to halve in value. Either way it assumes a constant rate and doesn't model market volatility — it's a quick sense-check, not a forecast.

Can I use the Rule of 72 for inflation?

Yes — the Rule of 72 works for anything that grows or shrinks at a compound rate, including inflation. At 3% annual inflation, your money's purchasing power halves in about 72 ÷ 3 = 24 years. At 5% inflation, it halves in about 14.4 years. This is a quick way to understand the impact of inflation: if you're 30 and inflation averages 3%, your savings will lose half their purchasing power by age 54. This is why holding large amounts of cash long-term is risky — even "modest" 3% inflation halves your purchasing power in under a generation. The Rule of 72 makes this intuitive without needing a spreadsheet.

How does the Rule of 72 relate to my retirement planning?

The Rule of 72 is one of the most powerful mental models for retirement planning. If you're 30 with $50,000 invested at 7%, it will double to $100,000 by 40, $200,000 by 50, $400,000 by 60, and $800,000 by 70 — without adding another dime. This is why starting early matters more than saving more later: a 25-year-old who invests $10,000 at 7% will have $160,000 by age 65 (4 doublings). A 45-year-old who invests the same $10,000 at 7% will only have $40,000 by 65 (2 doublings). The 20-year head start is worth $120,000 — far more than any extra contributions the 45-year-old could reasonably make. Use the Rule of 72 to quickly estimate your future portfolio and whether you're on track.

Is there a similar rule for tripling or quadrupling?

Yes! The Rule of 72 is just one of a family of "rules of thumb" for compound growth: Rule of 115 estimates how long it takes to triple your money (115 ÷ rate). At 7%, that's about 16.4 years. Rule of 144 estimates quadrupling (144 ÷ rate). At 7%, that's about 20.6 years. These work because ln(3) ≈ 1.0986 (scaled to 115) and ln(4) ≈ 1.386 (scaled to 144). You can also use the Rule of 72 iteratively: doubling twice = quadrupling, so 10.3 years × 2 = 20.6 years to quadruple at 7%. These mental shortcuts let you quickly estimate growth without a calculator — useful for evaluating investment opportunities, understanding inflation, and planning retirement.