Rule of 72 Calculator

How to use Rule of 72 Calculator

1. Pick a mode: years to double, or rate needed to double.
2. Enter an annual rate (or a number of years). Rates are examples you can change.
3. Compare the exact answer with the rule of 72, 70 and 69.3 estimates and their percentage errors.
4. Scan the table to see which shortcut is most accurate near your rate.

The exact formula and the shortcuts

If money grows by a fixed percentage r each year, after t years it has been multiplied by (1 + r)^t. Doubling means this equals 2, so t = ln(2) / ln(1 + r). That is the exact answer, which this page labels clearly. The shortcuts replace it with a constant divided by the percentage: 72 / rate, 70 / rate and 69.3 / rate (where 69.3 is 100 x ln 2, rounded). The reverse question uses r = 2^(1/t) - 1.

Worked example at 8 per cent: exact doubling takes ln(2) / ln(1.08) = 9.0065 years. The rule of 72 gives 72 / 8 = 9, an error of -0.07 per cent. The rule of 70 gives 8.75 and the rule of 69.3 gives 8.6625. To double in 10 years you need 2^(0.1) - 1 = 7.177 per cent a year, while 72 / 10 suggests 7.2 per cent. At 1 per cent the exact time is 69.66 years but the rule of 72 says 72, an error of +3.36 per cent.

Where it helps

The rule is a mental-maths tool for quickly comparing options. It shows why a small difference in return matters over decades: at 6 per cent money doubles in about 12 years, at 9 per cent in about 8. It also works against you, since inflation of 6 per cent halves purchasing power in about 12 years, and debt with a high interest rate can double just as fast. The same idea applies to population growth or the growth of a business.

• Use 72 for rates between about 6 and 10 per cent.
• Use 70 or 69.3 for low rates and continuous compounding.
• Use the exact formula for precision or for rates above 20 per cent.

Limits and privacy

The rule assumes a constant rate with all gains reinvested and no fees, taxes, deposits or withdrawals. Real returns vary year to year. For regular investments use a SIP or compound interest calculator instead, and for dated, irregular flows use an XIRR calculator. Calculations run in your browser and no data is sent anywhere. This is an educational tool, not financial advice.

Why use this rule of 72 calculator tool

• Exact next to the shortcuts. The exact value ln(2) / ln(1 + r) sits beside the 72, 70 and 69.3 approximations.
• Both directions. Find the time to double, or the annual rate you need to double in a chosen number of years.
• Error comparison table. Seventeen rates from 1 per cent to 36 per cent show how far each rule drifts from exact.
• Works for anything that compounds. Use it for savings, inflation, population or any steady percentage growth.

Frequently asked questions

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