Rule of 72 calculator

See how long money takes to double at a growth rate, by the rule of 72 and exactly, and how far apart the two are.

Doubling time · Compounding · Mental maths · Free

How long to double

Growth rate a year

Compounded once a year.

The rule

Starting amount

Years to show

The other way round

Years to double

Rate needed

12.25%

The rule of 72 says 12.0%: 72 ÷ 6.

Rule of 72

9.0 years

72 ÷ 8

Exact

9.01 years

ln 2 ÷ ln(1 + 8%)

The rule is off by

0.01 years

0.1% too short

1,000 compounding at 8% a year

Value, compounding exactly
Each doubling
Rule of 72

The value doubles every 9.01 years, 3 times in 30 years, to 10,063. The hollow markers are where the rule puts each doubling; the gap between the two grows with every one.

Growth rate: 8% a year
Compounding: Once a year
Starting amount: 1,000

The rule of 72 against the exact time, 1% to 15%

Rate	Rule, years	Exact, years	Gap
1%	72.0	69.66	+2.34
2%	36.0	35.00	+1.00
3%	24.0	23.45	+0.55
4%	18.0	17.67	+0.33
5%	14.4	14.21	+0.19
6%	12.0	11.90	+0.10
7%	10.3	10.24	+0.04
8%	9.0	9.01	−0.01
9%	8.0	8.04	−0.04
10%	7.2	7.27	−0.07
11%	6.5	6.64	−0.10
12%	6.0	6.12	−0.12
13%	5.5	5.67	−0.13
14%	5.1	5.29	−0.15
15%	4.8	4.96	−0.16

Reading the table

The rule of 72 is closest to exact near 8%, which is why it is the one bankers carry. Below it the rule says a doubling takes longer than it does, above it a little less. From 5% to 15% it is within a fifth of a year; at 1% it is more than two years out.

The rule of 69.3 is exact for continuous compounding and the rule of 70 sits between the two, closer at the low rates of inflation and population growth: at 1% the rule of 70 is a third of a year out.

To find the rate between two values rather than the time, use the CAGR calculator.

How it works

A value growing at a constant rate doubles when one plus the rate, raised to the number of years, reaches two. Solved for the years, that is the natural log of two over the natural log of one plus the rate: the exact doubling time.

The rule of 72 replaces that with 72 divided by the rate in per cent, which can be done in your head. At 8% it gives 9 years against an exact 9.01; it is closest near 8% and drifts slowly either side, which is why 72 is the number bankers carry rather than 69.3 or 70.

Run backwards, the rule gives the rate a doubling time needs: a value that doubles in six years has grown about 12% a year. For a growth rate between any two values, not just one and two, the compound annual growth rate is the same calculation in general form.

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