Rule of 72 Calculator

Last updated: 2026-05-13

The Rule of 72

The Rule of 72 is a mental-arithmetic shortcut that estimates how long it takes for an amount to double at a given annual rate of return. The estimate is 72 divided by the rate expressed as a percentage. At 6%, money doubles in roughly 12 years; at 9%, in 8 years; at 12%, in 6 years. The approximation requires no calculator, which is what makes it useful for quick comparisons.

How it's calculated

The mathematically precise doubling time uses natural logarithms:

where $r$ is the annual rate as a decimal and $r\%$ is the same rate as a percentage.

If 69.3 is the exact constant, why use 72? Convenience. 72 is divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36 — covering virtually every round interest rate encountered in practice. Mental division by 72 is fast and error-free. The trade-off is a small systematic overestimate (72 > 69.3) of about 3–4% at typical rates — acceptable for a planning heuristic.

Accuracy across rates

The rule is most accurate in the 6–10% range — which happens to cover the long-run historical return of a diversified stock market index. Below 6%, it overestimates slightly; above 10%, it underestimates slightly. In both cases the error stays within 5% for practical planning purposes.

Variations

The same construction works for any target multiple, with a different numerator. The numerator is the natural log of the target multiple multiplied by 100, rounded to a convenient divisor.

Rule of 70 — used interchangeably for doubling time, especially in macroeconomics and GDP-growth contexts. It is closer to the exact constant (69.3) but divides less neatly.

Rule of 114 — estimates tripling time: 114 ÷ rate%.

Rule of 144 — estimates quadrupling time: 144 ÷ rate%.

Applications

For investments, the rule turns a rate into an intuitive horizon. A savings account at 4.5% doubles in 72 ÷ 4.5 = 16 years, so the initial amount quadruples over two such periods (32 years). A stock market index returning 7% real doubles in 72 ÷ 7 ≈ 10.3 years: $10,000 invested at 7% real per year grows to roughly $150,000 over 40 years (close to four doublings, a roughly 15× growth factor). A diversified portfolio at 9% doubles in 8 years, which over a 40-year career is five doublings — a 32× growth factor before taxes and fees.

The rule works symmetrically for debt, since an unpaid balance compounds the same way savings do:

• Credit card at 20% APR: 72 ÷ 20 = 3.6 years for an unpaid balance to double
• Payday loan at 36%: 72 ÷ 36 = 2 years
• Student loan at 6%: 72 ÷ 6 = 12 years

A $5,000 credit-card balance compounding at 20% with no payments reaches $10,000 in 3.6 years and $20,000 in 7.2 years.

The rule also applies to inflation, where it estimates how long until purchasing power is cut in half. At 3% inflation, purchasing power halves in 72 ÷ 3 = 24 years; at 7%, in about 10 years. For a fixed income held through a long retirement, this halving is a material consideration: at 3% average inflation, a dollar's purchasing power roughly halves over 24 years.

Limitations

• The rule is calibrated for annual compounding at a fixed rate — neither of which holds in real life. More frequent compounding (monthly, daily) at the same stated rate produces slightly shorter doubling times than the annual formula suggests.
• Taxes and fees are not included. A fund earning 8% gross with 0.5% annual fees and effective 25% tax on gains has a real after-tax return much lower — and a much longer real doubling time.
• The rule is a planning heuristic, not a forecast. Actual investment returns vary year to year; the rule works on long-run averages.