Rule of 72 calculator

The rule of 72 estimates how long money takes to double: divide 72 by the yearly growth rate in percent. At 8% a year, 72 ÷ 8 = 9 years; the exact answer is 9.01 years. At 10% the rule says 7.2 and the exact time is 7.3 years.

Rule of 72: 9 years
Rule of 70: 8.75 years
Exact (ln 2 ÷ ln(1 + rate)): 9.01 years
Rule of 72 minus exact: −0.01 years

The rate to double in a number of years

Rule of 72 (72 ÷ years): 12%
Exact rate: 12.25%

Formula

Years to double ≈ 72 ÷ Rate (in percent)
Rate to double in N years ≈ 72 ÷ N
Exact years to double = ln 2 ÷ ln(1 + Rate)
Rule of 70: Years ≈ 70 ÷ Rate

Worked example

Assume an investment doubles every 7 years. How many years does it take to grow from $3,000 to $24,000?

$24,000 ÷ $3,000 = 8.
8 = 2 × 2 × 2: three doublings.
3 × 7 = 21 years.

Answer: 21

From the lesson CAGR & Doubling.

Do it in your head: Rule of 72 and doublings

How long money takes to double, or to grow 8 times.

Years to double ≈ 72 ÷ the rate (8 for 8%). Backward, the rate ≈ 72 ÷ the years.
Count the doublings in the multiple: 8 is 2 × 2 × 2, three doublings.
Multiply the doublings by the doubling time.

How far the rule of 72 drifts

Exact years to double = ln 2 ÷ ln(1 + rate). Error = (rule − exact) ÷ exact.

How far the rule of 72 drifts
Rate	Rule of 72	Rule of 70	Exact	Rule of 72 error
1%	72	70	69.66	3.4%
2%	36	35	35	2.8%
3%	24	23.33	23.45	2.3%
4%	18	17.5	17.67	1.9%
5%	14.4	14	14.21	1.4%
6%	12	11.67	11.9	0.9%
7%	10.29	10	10.24	0.4%
8%	9	8.75	9.01	−0.1%
9%	8	7.78	8.04	−0.5%
10%	7.2	7	7.27	−1%
12%	6	5.83	6.12	−1.9%
15%	4.8	4.67	4.96	−3.2%
18%	4	3.89	4.19	−4.5%
20%	3.6	3.5	3.8	−5.3%
25%	2.88	2.8	3.11	−7.3%
30%	2.4	2.33	2.64	−9.2%

Try three

Assume money grows 24% a year. Using the rule of 72, about how many years does it take to double?

Your answer
Show the answer
3
1. Years to double ≈ 72 ÷ rate = 72 ÷ 24 = 3.
2. It's an estimate: closest for rates near 8%, and further off at very low or very high rates.
Assume an investment doubles every 3 years. How many years does it take to grow from $30,000 to $60,000?

Your answer
Show the answer
3
1. $60,000 ÷ $30,000 = 2: one doubling.
2. 1 doubling × 3 years = 3 years.
Assume money grows 6% a year. Using ln 2 ≈ 0.6931 and ln 1.06 ≈ 0.05827, how many years does it take to double, allowing fractional years? Round to one decimal place.

Your answer
Show the answer
11.9
1. Solve 1.06ᵗ = 2 with logs: t = ln 2 ÷ ln 1.06 = 0.6931 ÷ 0.05827 ≈ 11.9 years.
2. If growth is only credited once a year, the first year-end at or above double is year 12.

That’s the idea. Keep going: 4 warm-up problems, no sign-up →

Learn it properly: CAGR & Doubling → · the course: CAGR & Doubling

Related lessons: Compound Growth

Questions

Why 72?

The exact doubling time is ln 2 ÷ ln(1 + r). For small rates ln(1 + r) is close to r, which gives about 69.3 ÷ the rate in percent. 72 is a little higher, which fits typical rates of 6% to 10% better, and it divides evenly by 2, 3, 4, 6, 8, 9 and 12.

How accurate is the rule of 72?

Within a few percent between 3% and 15% a year: at 8% it says 9 years and the truth is 9.01. It drifts at high rates: at 30% it says 2.4 years, but money doubles in 2.64.

When should I use the rule of 70?

For low rates like inflation or population growth, around 1% to 3%, where 70 is closer to the exact answer.

Can I use it backward?

Yes. To double in 6 years you need about 72 ÷ 6 = 12% a year (exactly 12.2%).

How do I count several doublings?

Count the doublings in the multiple, then multiply by the doubling time. Growing 8 times is three doublings (2 × 2 × 2), so at 7 years per doubling it takes 21 years.

Related free tools

Formulas and examples checked against Doing Math’s verified lesson CAGR & Doubling, September 27, 2026. Every number on this page is computed by the calculator’s own code.