Free calculator

Rule of 72 Calculator

Estimate years to double your money at a given rate. Compare the Rule of 72 shortcut with the exact compound formula.

Calculator

Annual rate (%) Positive rate for years to double

Compounds per year Used for the exact doubling time

Rule of 72 (years) n/a

Exact years n/a

Difference n/a

How long to double your money
Rate	Exact years	Rule of 72
1%	69.3	72.0
2%	34.7	36.0
3%	23.1	24.0
4%	17.4	18.0
5%	13.9	14.4
6%	11.6	12.0
7%	9.9	10.3
8%	8.7	9.0
10%	7.0	7.2
12%	5.8	6.0
15%	4.6	4.8
20%	3.5	3.6

Exact years use ln(2) ÷ (n × ln(1 + r ÷ n)) with the compounding frequency above. Default table is monthly (n = 12). Rule of 72 is always 72 ÷ rate%.

How do you use the Rule of 72?

Years to double ≈ 72 ÷ rate%. At 6%, about 12 years. Exact compounding is ln(2) ÷ ln(1 + rate).

Does the Rule of 72 work for inflation?

Yes as a napkin for years until prices double (or purchasing power halves): 72 ÷ inflation%.

How long does it take to triple or quadruple your money?

Use 114 ÷ rate% to triple and 144 ÷ rate% to quadruple. At 6% that gives 19 and 24 years, against an exact 18.9 and 23.8 with annual compounding.

When does the Rule of 72 go wrong?

At the extremes. With annual compounding it says 72 years at 1% against an exact 69.7, and 1.4 years at 50% against an exact 1.7. In the middle it is a very good napkin.

Can you use the Rule of 72 backwards?

Yes. Rate% ≈ 72 ÷ years. To double in 9 years you need about 8% a year (exactly 8.01%). It also works on debt, which is less fun.

Years to double, triple and quadruple your money

Exact years with annual compounding: ln(multiple) ÷ ln(1 + rate). Rates are examples, not forecasts.

Rate	Double	Triple	Quadruple
2%	35.0	55.5	70.0
4%	17.7	28.0	35.3
6%	11.9	18.9	23.8
8%	9.0	14.3	18.0
10%	7.3	11.5	14.5
12%	6.1	9.7	12.2
15%	5.0	7.9	9.9

The formula

Rule of 72 (shortcut):
Years ≈ 72 ÷ rate%

Exact years to double with compounding n times a year:
Years = ln(2) ÷ (n × ln(1 + rate ÷ n))
Annual compounding is the special case n = 1: ln(2) ÷ ln(1 + rate).

rate is a decimal (6% = 0.06). The rule is a napkin shortcut.

Worked example

At 6% a year:

Rule of 72: 72 ÷ 6 = 12 years.

Exact: ln(2) ÷ ln(1.06) ≈ 11.90 years.

At 10%:

Rule: 72 ÷ 10 = 7.2 years.

Exact: ln(2) ÷ ln(1.10) ≈ 7.27 years.

Close enough for a napkin. Not close enough for a term sheet.

Methodology

How it calculates

Shows the napkin Rule of 72 estimate next to the exact compound doubling time.

Formula

Rule of 72 (shortcut):
Years ≈ 72 ÷ rate%
Exact years to double with compounding n times a year:
Years = ln(2) ÷ (n × ln(1 + rate ÷ n))
Annual compounding is the special case n = 1: ln(2) ÷ ln(1 + rate).
rate is a decimal (6% = 0.06). The rule is a napkin shortcut.

Assumptions

Rule of 72 is an approximation. Exact path uses continuous ln maths with your compounding choice.

Edge cases

At very high or very low rates the napkin rule drifts from the exact figure.

Sources

None. Pure maths; no external rate or spec feed.

FAQ

Why 72 and not 69 or 70?

ln(2) is about 0.693, so 69.3 ÷ rate% is nearer the continuous case. 72 divides neatly by 2, 3, 4, 6, 8, 9 and 12, so it won the pub-math contest.

Does the rule work for inflation too?

Yes, as a rough half-life of purchasing power. At 3% inflation, 72 ÷ 3 ≈ 24 years for prices to double.

What about monthly compounding?

Pick Monthly (12) in Compounds per year. Exact years then use ln(2) ÷ (n × ln(1 + rate ÷ n)). The Rule of 72 column stays 72 ÷ rate%.

Not financial advice. This calculator is for education only. Double-check results before you make money decisions. Past moves do not predict future ones.