Rule of 72 Calculator

What formulas does this tool use?

This tool uses years ≈ 72 ÷ rate and rate ≈ 72 ÷ years for the Rule of 72 rows. For comparison it also computes the exact values: years = ln 2 ÷ ln(1 + rate ÷ 100) and rate = (2^(1 ÷ years) − 1) × 100. A third row uses 69.3 in place of 72.

Is the rate entered as a percentage?

Yes. In “years to double” mode, 8 means 8% a year. In “rate needed” mode, the same box holds the number of years. Only one box exists, so check the mode selector before reading the answer.

How close is 72 to the exact answer?

It depends on the rate. At 8% the rule gives 9.00 years against 9.01 exact. At 3% it gives 24.00 against 23.45, at 12% 6.00 against 6.12, and at 20% 3.60 against 3.80. The rule is nearest to exact around 8% and drifts either side of it.

What is the 69.3 row for?

It is the figure 100 × ln 2 rounded, which is the exact answer for continuous compounding and a better approximation than 72 at low rates. At 1% it gives 69.30 years against 69.66 exact, while 72 gives 72.00. Rates near 8% suit 72 best.

What does it show for 0 or negative inputs?

An error message asking for a positive value. A 0% rate never doubles the money, and negative growth means it shrinks, so there is no doubling time to display. The tool does not output infinity.

What compounding does it assume?

Once a year. The exact rows use (1 + rate)^years, so they describe annual compounding. More frequent compounding would double the money slightly sooner, and the tool has no frequency setting.

Can it handle tripling, taxes, fees or inflation?

No. It only answers when money doubles, with a constant rate and no deposits, charges, tax or price changes. The figures are a quick arithmetic illustration, not a forecast, and it never states what return any asset will earn.