Rule of 72 Calculator
Find out how long it takes money to double at any interest rate using the classic mental math shortcut, and compare against the exact logarithmic formula. Also solves the reverse: what rate do you need to double in a target number of years.
Last updated: April 2026
7% is the standard real stock market return
How the Rule of 72 works
Exact formula: years = ln(2) / ln(1 + r)
where r is rate as decimal (0.07 for 7%)
The Rule of 72 comes from the math of natural logarithms. The exact formula for doubling time is ln(2) / ln(1 + r), and ln(2) ≈ 0.6931. For small interest rates, ln(1 + r) ≈ r, so the formula simplifies to 0.6931 / r, or 69.31 / rate as a percent.
Why 72 instead of 69? Two reasons. First, 72 is divisible by many common rates (2, 3, 4, 6, 8, 9, 12), making mental math trivial. At 6%, 72/6 = 12 — clean integer math. Second, at the typical rates investors encounter (6-10%), the curvature of the logarithm makes 72 slightly more accurate than 69. The rule is a happy accident of number theory meeting practical math.
The rule works in both directions. To find the rate needed to double in a target number of years, divide 72 by the years. Want to double in 8 years? You need 72/8 = 9% annual return. Want to double in 6 years? You need 12%. This makes the rule useful not just for estimating growth but for setting return targets.
Full doubling time table
| Interest rate | Rule of 72 | Exact formula | Rule of 72 error |
|---|---|---|---|
| 1% | 72.0 years | 69.7 years | +3.3% |
| 2% | 36.0 years | 35.0 years | +2.8% |
| 3% | 24.0 years | 23.4 years | +2.4% |
| 4% | 18.0 years | 17.7 years | +1.8% |
| 5% | 14.4 years | 14.2 years | +1.4% |
| 6% | 12.0 years | 11.9 years | +0.9% |
| 7% | 10.3 years | 10.2 years | +0.5% |
| 8% | 9.0 years | 9.0 years | +0.1% |
| 9% | 8.0 years | 8.0 years | -0.2% |
| 10% | 7.2 years | 7.3 years | -0.6% |
| 12% | 6.0 years | 6.1 years | -1.2% |
| 15% | 4.8 years | 5.0 years | -3.1% |
| 20% | 3.6 years | 3.8 years | -5.5% |
| 25% | 2.88 years | 3.11 years | -7.3% |
The Rule of 72 is most accurate between about 5% and 15%, where it is within 1% of the exact formula. Outside that range, it drifts — overestimating doubling time at low rates and underestimating at high rates.
Three ways to use the Rule of 72
1. Investment growth planning
At 7% real return (the long-term S&P 500 average), your money doubles every ~10.3 years. Starting with $100,000 at age 30: $200K by 40, $400K by 50, $800K by 60, and $1.6M by 70. Each doubling is bigger than the last — which is why starting early is so valuable. Miss the first doubling by starting at 40, and you lose the final doubling from $800K to $1.6M at the end.
2. Inflation impact
At 3% inflation (US long-term average), prices double every 24 years. At 6% inflation (Venezuela 2014, US early 1980s), prices double every 12 years. At 10% inflation (Turkey 2022), prices double in just 7.2 years. This is why fixed-income retirees suffer during inflationary periods — their purchasing power halves on a schedule. Use the Rule of 72 to understand how much your future dollars will actually buy.
3. Debt compounding
Credit card debt at 22% APR doubles in 72/22 = 3.3 years if unpaid. At 15% APR, in 4.8 years. At 29.99% APR (store cards), in 2.4 years. This is why the minimum payment trap is so vicious — even moderate credit card rates cause balances to explode on a short timeline. Seeing the doubling interval is sometimes more motivating than staring at a raw APR number.
Frequently asked questions
What is the Rule of 72?
The Rule of 72 is a mental math shortcut for estimating how long it takes an investment to double at a given annual interest rate. Divide 72 by the rate (as a percent) to get the approximate doubling time in years. At 8% interest, money doubles in 72/8 = 9 years. At 6%, it doubles in 12 years. At 12%, it doubles in 6 years. The rule is widely taught in finance classes because it enables quick mental math without a calculator, and it is accurate enough for most practical purposes.
Why does the Rule of 72 work?
It comes from the math of natural logarithms. The exact formula for doubling time is ln(2) / ln(1 + r), where r is the rate as a decimal. ln(2) ≈ 0.693 or about 69.3%. For small rates, ln(1 + r) ≈ r, which means doubling time ≈ 69.3 / rate. The number 72 is used instead of 69.3 because (a) 72 is divisible by many common integer rates (2, 3, 4, 6, 8, 9, 12), making mental math easier, and (b) at typical rates of 6-10%, 72 gives a slightly more accurate approximation than 69.3 due to the curvature of the logarithm.
How accurate is the Rule of 72?
Very accurate for rates between about 5% and 15%. Outside that range, it drifts. At 1%, the Rule of 72 says 72 years to double; the exact answer is 69.7 years — a 3.3% overestimate. At 25%, Rule of 72 says 2.88 years; exact is 3.11 years — a 7% underestimate. For the rates most investors encounter (5-15%), the Rule of 72 is within 1-2% of exact. That is plenty accurate for mental planning.
What is the Rule of 70?
The Rule of 70 is a more accurate version for lower interest rates. Divide 70 by the rate to get doubling time. It tracks closer to the exact formula at rates under 6%. For example, at 3% interest, Rule of 70 gives 23.3 years; exact is 23.4 years. At the same rate, Rule of 72 gives 24 years — slightly further from truth. For higher rates (8-12%), Rule of 72 actually outperforms Rule of 70. In practice, most people use 72 because it divides more evenly.
What is the Rule of 69 or Rule of 69.3?
The Rule of 69 (sometimes 69.3) is the most mathematically accurate version for continuous compounding. It comes directly from ln(2) ≈ 0.693. It is more accurate than Rule of 72 at low rates and for continuous compounding, but less practical for mental math since 69 is not divisible by many integers. You'll see Rule of 69 in academic finance contexts and Rule of 72 in everyday use.
Who invented the Rule of 72?
The earliest known reference is in Luca Pacioli's 1494 book "Summa de Arithmetica," though Pacioli did not derive the formula — he just mentioned it as a rule of thumb traders already used. The rule predates formal calculus and logarithms. Some sources trace it to earlier Italian merchants. It has been a finance staple for over 500 years because it enables quick mental math without requiring any advanced calculation.
Can I use Rule of 72 for inflation?
Yes, and it is one of the most useful applications. Divide 72 by the inflation rate to find out how long it takes prices to double (or your purchasing power to halve). At 3% inflation, prices double in 24 years. At 6% inflation, prices double in 12 years. At 10% inflation (like the early 1980s), prices double in just 7.2 years. This is why inflation is called the "silent killer" of long-term savings — even modest rates compound to dramatic erosion of purchasing power over a retirement timeline.
Can I use Rule of 72 for negative returns?
Yes. Divide 72 by the loss rate to find out how long it takes money to halve. At -5% annual return, money halves in 14.4 years. At -10%, in 7.2 years. This is useful for understanding how fast losses compound. It also applies to real returns during inflationary periods: cash at -3% real return halves in purchasing power in 24 years.
What is the Rule of 144?
The Rule of 144 estimates how long it takes money to quadruple (4x). Divide 144 by the rate. At 8%, money quadruples in 18 years. The logic: doubling twice = 4x, so 72 + 72 = 144. Similarly, the Rule of 115 estimates tripling time (since ln(3) / ln(2) ≈ 1.585, and 72 × 1.585 ≈ 114). At 8%, money triples in 115/8 ≈ 14.4 years.
Should I use the exact formula or the rule of 72?
For mental math in casual conversation, use the Rule of 72. For presentations, spreadsheets, or any serious financial planning, use the exact formula: years = ln(2) / ln(1 + r). Spreadsheets make this trivial — in Excel or Google Sheets, the formula is =LN(2)/LN(1+r) where r is the rate as a decimal. This calculator shows both so you can see how close the Rule of 72 estimate is to the exact answer.
How does the Rule of 72 apply to investing?
The most common application is understanding how your retirement portfolio grows. If you expect 7% real returns in stocks, your money doubles every 10.3 years. A $100,000 portfolio becomes $200,000 in 10 years, $400,000 in 20, $800,000 in 30, $1.6M in 40. This is why starting early matters so much — each doubling matters more than the last. Miss the first doubling by starting 10 years late, and you lose the compounding of the largest final doublings.
Does the Rule of 72 work for debt too?
Yes. If you carry a credit card balance at 22% APR and make no payments, the debt doubles in 72/22 = 3.3 years. At 15% APR, it doubles in 4.8 years. This is why credit card debt is so punishing — even moderate rates cause debt to double in under a decade. The Rule of 72 gives a visceral sense of how fast unchecked debt can spiral, which is sometimes more motivating than staring at a raw interest figure.
Methodology: Calculator shows both the Rule of 72 estimate (72 / rate) and the exact doubling time from the logarithmic formula ln(2) / ln(1 + r). The error percentage is calculated as (Rule of 72 - Exact) / Exact × 100.
Historical note: The Rule of 72 appears in Luca Pacioli's 1494 "Summa de Arithmetica," though Pacioli describes it as an existing practice among Italian merchants, not something he invented.
Disclaimer: This calculator is for educational purposes only and is not investment advice.