Rule of 72 Calculator: How Long to Double Your Money

How to use the calculator

Choose what to find: Years if you know the rate, or Rate if you know how many years you have.
Enter the annual rate (for example 8 for 8%) or the number of years.
Pick the multiple: 2× to double, 3× to triple or 4× to quadruple.

You get the rule-of-thumb answer, the exact answer with yearly compounding, the answer with continuous compounding, and how far off the rule is. The rule of 70 and rule of 69.3 results appear only for doubling. The table lists every approximation for rates from 1% to 20%.

The formulas

With a rate of r% a year and a target multiple m:

Rule of thumb: years ≈ constant ÷ r, with 72 for doubling, 114 for tripling and 144 for quadrupling.
Exact, compounded yearly: years = ln(m) ÷ ln(1 + r/100)
Continuous compounding: years = 100 × ln(m) ÷ r. For doubling, 100 × ln 2 = 69.31, which is where the rule of 69.3 comes from.
Rate needed in N years: exact m^(1/N) − 1; rule: constant ÷ N.

The rule error is (rule − exact) ÷ exact: negative means the shortcut is too optimistic, positive means it's too cautious.

Examples

1. Doubling at 8%

72 ÷ 8 = 9 years. The exact answer with yearly compounding is 9.006 years, so the rule is off by just −0.07%. The rule of 70 gives 8.75 years and the rule of 69.3 gives 8.66.

2. What rate doubles money in 10 years?

The rule says 7.2%; the exact rate is 7.18%.

3. Tripling and quadrupling

At 6%, the rule of 114 says money triples in 19 years; exactly, it takes 18.85. At 10%, the rule of 144 says it quadruples in 14.4 years, against an exact 14.55.

4. How accurate each rule is for doubling

Rate	Rule of 72	Rule of 70	Rule of 69.3	Exact
2%	36.00	35.00	34.65	35.00
4%	18.00	17.50	17.33	17.67
6%	12.00	11.67	11.55	11.90
8%	9.00	8.75	8.66	9.01
10%	7.20	7.00	6.93	7.27
12%	6.00	5.83	5.78	6.12
20%	3.60	3.50	3.47	3.80

Which rule to trust

With yearly compounding, the rule of 70 is closer at low rates (up to about 4%), and the rule of 72 is closer from about 5% upward, nearly exact around 8%. At high rates every shortcut undershoots: at 20%, 72 gives 3.6 years against an exact 3.80, an error of −5.3%. The rule of 69.3 matches continuous compounding rather than yearly compounding. The constant 72 is popular partly because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes mental math easy.

Frequently asked questions

How accurate is the rule of 72?

Very close for typical rates. Between about 5% and 12% it stays within a few tenths of a year of the exact answer, as the table shows. It is an approximation; use the exact figure for planning.

Can I use the rule of 72 for inflation?

Yes: it estimates how long it takes prices to double, or the purchasing power of a dollar to halve. The U.S. Bureau of Labor Statistics reported that the CPI-U rose 3.4% in the 12 months to August 2026. If that rate continued, the rule says prices would double in about 21.2 years; exactly, 20.73.

Does it work for debt?

The math is the same: an unpaid balance growing 20% a year doubles in about 3.8 years with yearly compounding. If interest compounds more often than once a year, it doubles faster still.

What are the rule of 114 and rule of 144?

The same idea for tripling and quadrupling: divide 114 or 144 by the annual rate. Because quadrupling is doubling twice, 144 is simply 2 × 72.

Does the rule of 72 guarantee my money will double?

No. It assumes a constant rate every year. Investment returns vary and can be negative, so the years it gives are a rough guide, not a promise.

Sources

This calculator is for educational purposes and is not investment advice. It assumes a constant rate of growth, which real investments do not deliver.

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