The rule of 72 is the quickest way to feel the power of compound growth: divide 72 by the yearly rate, and you have roughly the number of years it takes money to double. This calculator gives that shortcut answer, the exact answer and the continuous-compounding answer side by side, and it works the other way too — telling you the rate you would need to double, triple or quadruple your money by a deadline.
How to use the rule of 72 calculator
- Choose whether to find the years to grow at a given rate or the rate needed within a number of years.
- Enter the annual rate of return or the years available.
- Pick the goal: double, triple or quadruple.
- Optionally enter a starting amount to see what it grows to.
- Compare the rule’s estimate with the exact figures, the chart and the table of common rates.
Rule of 72 formulas
The shortcut:
The exact doubling time with yearly compounding, and with continuous compounding:
For tripling and quadrupling, replace 72 with 114 or 144, and ln 2 with ln 3 or ln 4.
Worked example
You expect an 8% average annual return on $10,000.
Rule of 72: 72 ÷ 8 = 9 years to reach $20,000
Exact with yearly compounding: ln 2 ÷ ln 1.08 = 0.693147 ÷ 0.076961 = 9.006 years
Continuous compounding: 0.693147 ÷ 0.08 = 8.664 years
Working backward: to double money in 9 years you need about 72 ÷ 9 = 8% a year; the exact figure is 21/9 − 1 = 8.006%.
How good is the shortcut?
| Rate | Rule of 72 | Rule of 69.3 | Exact (yearly) |
|---|---|---|---|
| 2% | 36.00 | 34.65 | 35.00 |
| 4% | 18.00 | 17.32 | 17.67 |
| 6% | 12.00 | 11.55 | 11.90 |
| 8% | 9.00 | 8.66 | 9.01 |
| 10% | 7.20 | 6.93 | 7.27 |
| 15% | 4.80 | 4.62 | 4.96 |
| 20% | 3.60 | 3.47 | 3.80 |
The number 72 is popular because it is close to the exact answer for typical investment returns and divides evenly by 2, 3, 4, 6, 8, 9 and 12. The rule has a long history — it appears in Luca Pacioli’s 1494 mathematics textbook, centuries before calculators.
Practical uses
Investing
A portfolio earning 6% doubles about every 12 years. Starting at 25 instead of 37 means one extra doubling by 61 — the same money ending up twice as large.
Inflation
At 3% inflation, prices double in about 24 years (exactly 23.4). Retirement plans need to account for that loss of purchasing power; the inflation calculator uses actual CPI history.
Debt
The rule works against you too. A credit card balance at 24% APR left unpaid would roughly double in three years.
Fees
A 1% annual fee on a 7% return cuts the rate to 6% and stretches the doubling time from about 10.3 to 12 years.
For precise projections with contributions, use the compound interest calculator.
The rule of 72 is an approximation, and investment returns are not steady from year to year. Use the results for intuition and planning, not as guarantees.
Frequently asked questions
What is the rule of 72?
It is a mental-math shortcut: divide 72 by the annual percentage rate to estimate how many years it takes an investment to double. At 8%, 72 ÷ 8 = 9 years. The exact answer with yearly compounding is 9.006 years.
How accurate is the rule of 72?
It is very close for rates between about 6% and 10%, where the error is well under 1%. It overstates the time at low rates and understates it at high rates; at 2% it gives 36 years versus an exact 35.0, and at 20% it gives 3.6 versus 3.8.
What are the rules of 70 and 69.3?
They are variations that fit continuous compounding better, because ln 2 ≈ 0.693. The rule of 69.3 is nearly exact for continuous growth, and the rule of 70 is popular for quick estimates of population or economic growth at low rates.
Can I use the rule of 72 for inflation or debt?
Yes. At 3% inflation, prices double — and a dollar's purchasing power halves — in about 72 ÷ 3 = 24 years. Unpaid credit card debt at 24% would double in roughly 3 years.
How do I estimate tripling or quadrupling time?
Use 114 for tripling and 144 for quadrupling. At 8%, money roughly triples in 114 ÷ 8 = 14.25 years and quadruples in 144 ÷ 8 = 18 years — quadrupling is simply doubling twice.