Rule of 72 Calculator

How it works

The rule of 72 says money growing at a fixed annual rate doubles in about 72 ÷ rate years: at 8% a year, 72 ÷ 8 = 9 years. Turned around, doubling in a set number of years needs about 72 ÷ years percent a year.

The exact doubling time at a rate compounded once a year is ln 2 ÷ ln(1 + rate). The rule replaces that with a division you can do in your head, and 72 is used because it is close to the exact answer for everyday rates and divides evenly by 2, 3, 4, 6, 8, 9 and 12.

The estimate is closest around 8%. Below that it slightly overstates the time, and well above it understates it; the difference is shown next to the exact figure.

For tripling, the same shortcut uses 114: 72 × log₂ 3 ≈ 114.1, because tripling takes log₂ 3 ≈ 1.585 times as long as doubling. It is derived from the rule of 72, not a separate rule, so it is accurate at the same rates.

Formula

years to double ≈ 72 ÷ rate%      years to triple ≈ 114 ÷ rate%
rate to double  ≈ 72 ÷ years      rate to triple  ≈ 114 ÷ years   (in %)
exact years = ln m ÷ ln(1 + rate)   (m = 2 or 3)
exact rate  = m^(1 ÷ years) − 1

Example

At 8% a year, the rule of 72 gives 72 ÷ 8 = 9 years to double. The exact time is ln 2 ÷ ln 1.08 = 9.01 years. At 9%, it gives 8 years against an exact 8.04.

At 6%, the rule gives 12 years against an exact 11.90. To double in 10 years, the rule asks for 7.2% a year; the exact rate is 7.18%.

To triple at 10% a year, the rule of 114 gives 11.4 years; the exact time is ln 3 ÷ ln 1.1 = 11.53 years.

Assumptions and limitations

• The rate is fixed and compounded once a year, with nothing added or withdrawn. More frequent compounding doubles slightly sooner.
• The rule is an estimate for mental arithmetic; use the exact figure for planning.
• A rate you enter is an assumption, not a forecast. Taxes, fees and inflation are ignored.
• The result is for information and planning and is not financial, tax or investment advice.

Frequently asked questions