Rule of 72 Calculator

Calculate how long it takes to double your investment using the Rule of 72, 69, and 70. Enter your annual return rate to see the comparison.

Annual Return Rate (%)

Principal Amount ($)

Doubling Time Comparison at 8% annual return

Method	Formula	Years to Double
Rule of 72	72 ÷ r	9.00
Rule of 69	69.3 ÷ r	8.66
Rule of 70	70 ÷ r	8.75
Exact (ln 2)	ln(2) ÷ ln(1 + r/100)	9.0065

$10,000

Starting Amount

$20,000

Doubled Value (in ~9.0 yrs)

Years to Double at Common Rates

Rate	Rule of 72	Exact
2%	36.0 yrs	35.00 yrs
4%	18.0 yrs	17.67 yrs
6%	12.0 yrs	11.90 yrs
8%	9.0 yrs	9.01 yrs
10%	7.2 yrs	7.27 yrs
12%	6.0 yrs	6.12 yrs

About the Rule of 72 Calculator

The Rule of 72 is a mental math shortcut: divide 72 by the annual return rate to estimate how many years it takes to double an investment with compound interest. For example, at 8% return: 72 ÷ 8 = 9 years. The Rule of 69.3 is more accurate for continuous compounding, while the Rule of 70 is common in economics for GDP and inflation doubling. The exact formula uses the natural logarithm: ln(2) ÷ ln(1 + r/100).

Built and maintained by Meet Shah · Last updated 1 August 2026

What this tool is used for

Getting a quick mental estimate of a doubling time.
Comparing the 69, 70 and 72 variants to see where each is most accurate.
Explaining compounding to someone without a spreadsheet.
Sanity-checking a projection's doubling claim.
Estimating how inflation halves purchasing power over time.

Frequently Asked Questions

Where does 72 come from?: From the doubling equation ln(2)/ln(1+r), which for small rates approximates to 0.693/r. Using 69.3 would be exact at continuous compounding, but 72 divides evenly by 2, 3, 4, 6, 8, 9 and 12 — chosen for mental arithmetic rather than accuracy.
How accurate is it?: Within a few percent between roughly 4% and 15%, which covers most real returns. At 8% it gives 9 years against an exact 9.006; at 2% it says 36 where the answer is 35.0, and at 25% it says 2.88 where the truth is 3.1. The error grows at both extremes.
Does it work for inflation too?: Yes, and it is arguably more useful there — 72 divided by the inflation rate is how long until prices double. At 3%, that is 24 years, which is the clearest way to make a long-horizon projection feel real rather than abstract.
What are the rules of 114 and 144?: The same trick for tripling and quadrupling. 114 divided by the rate gives years to triple, 144 gives years to quadruple — 144 being 72 twice, since quadrupling is doubling twice over. They follow from the same logarithm.
Should I use 72 or 70?: 70 is closer for continuous compounding and low rates, and 72 is better for annual compounding in the ordinary range — plus far easier to divide in your head. The difference is under a year for anything you would use it on.

Common errors and gotchas

Using it at high rates, where the approximation drifts substantially from the real answer.
Treating the estimate as exact, when it is a rule of thumb by design.
Forgetting to use a real rather than a nominal rate when inflation matters.
Applying it to a variable return as if it were fixed.
Confusing the doubling of a balance with the doubling of purchasing power.