How accurate is the Rule of 72?

Very accurate in the commonly cited 6-10% range, but it drifts further from the actual doubling time at very low or high rates.

Can I use this for things other than investments?

Yes — the same math applies to any steadily compounding quantity.

What's the difference between the Rule of 72 and the exact formula?

The Rule of 72 is a linear approximation; the exact formula solves the real exponential equation using natural logarithms.

Does compounding frequency matter here?

This tool assumes the rate you enter is the effective annual rate already.

Is there a 'Rule of 114' or similar for tripling?

Yes — similar rules exist for tripling (Rule of 114) or quadrupling (Rule of 144).

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Finance

Rule of 72 Calculator

The 72÷rate doubling-time shortcut, compared against the exact compound-interest answer.

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Last reviewed 2026-08-30

About the Rule of 72 Calculator

Compares the Rule of 72 — a classic mental-math shortcut for estimating how many years it takes an investment to double — against the actual, precise doubling time from the real compound-interest formula, showing exactly how close the shortcut is at your specific rate.

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How to use it

Enter an annual interest or growth rate (%).
Read the Rule of 72 estimate alongside the actual precise doubling time.

Formula

Rule of 72 estimate (years) = 72 ÷ annual rate. Actual precise doubling time (years) = ln(2) ÷ ln(1 + rate).

Worked example

At an 8% annual rate: the Rule of 72 estimates 9.0 years to double; the actual precise doubling time is about 9.01 years — a difference of only about -0.06 years.

Rule of 72 accuracy by rate (exact formula)

Rule of 72 accuracy by rate (exact formula)
Annual rate	Rule of 72 estimate	Actual doubling time	Difference
2%	36.0 years	35.00 years	+1.00 years
4%	18.0 years	17.67 years	+0.33 years
6%	12.0 years	11.90 years	+0.10 years
8%	9.0 years	9.01 years	−0.01 years
10%	7.2 years	7.27 years	−0.07 years
12%	6.0 years	6.12 years	−0.12 years
20%	3.6 years	3.80 years	−0.20 years

Interpreting your result

The Rule of 72 is most accurate in the commonly cited 6-10% range. It gets noticeably less precise at very low rates (under ~2%) or very high rates (above ~20%). 69.3 is actually the more mathematically exact numerator for continuous compounding; 72 is preferred because it divides evenly by more small whole numbers.

Recommendations

• The Rule of 72 works for anything that compounds at a steady rate — investment returns, inflation, or population/revenue growth.
• For rates far outside the 6-10% sweet spot, check the actual precise doubling time shown here.
• A 'Rule of 70' or 'Rule of 69.3' exist as alternatives — 69.3 is more precise, but 72's easy divisibility makes it the most commonly taught version.

Frequently asked questions

72 divides evenly by more small whole numbers than the mathematically more precise 69.3, making it easier to compute mentally.