What is the Rule of 72?

A mental-math shortcut for compound growth: divide 72 by the annual percentage rate to estimate the number of years an investment takes to double.

How accurate is the Rule of 72?

Very close for rates between about 6% and 10% (within a few weeks of the exact answer). Outside that band the approximation drifts further from the exact log-based doubling time.

What is the exact formula?

Exact doubling time = ln(2) ÷ ln(1 + r), where r is the rate as a decimal. This is the precise inverse of the compound-growth formula, with no approximation.

Can I use it to find the rate needed to double in N years?

Yes — rearrange to rate ≈ 72 ÷ years for a quick estimate, or use the exact form 2^(1/years) − 1 for the precise rate; doubling money in 10 years needs about 7.18% exactly, versus 7.2% from the shortcut.

Does the Rule of 72 work for tripling or quadrupling money?

Not directly — those use the Rule of 114 (triple) and Rule of 144 (quadruple) respectively, following the same ln(n)/ln(1+r) logic with n = 3 or 4 instead of 2.

Why does a higher rate reduce the shortcut's accuracy?

The Rule of 72 is a linear approximation to a logarithmic relationship; the two curves are closest together near 8% and diverge more the further the rate sits from that point in either direction.

Stocks & Investing

Rule of 72 Calculator

Calculate how long an investment takes to double at a given annual rate using the Rule of 72 shortcut, compared against the exact compounding formula.

The Rule of 72 is a shortcut estimating the years needed to double an investment by dividing 72 by the annual percentage rate of return.

Years to double (Rule of 72)

9 yrs

Exact doubling time: 9.01 yrs
Shortcut error: -0.006 yrs

Rule of 72 = 72 ÷ rate. Most accurate for rates roughly between 6% and 10%.

Worked example

An investment compounds at 8% a year.

Rule of 72 estimate: 72 ÷ 8 = 9 years
Exact doubling time: ln(2) ÷ ln(1.08) = 9.01 years
Shortcut error: 9 − 9.01 ≈ −0.01 years (about 2 days)

The Rule of 72 says 9 years to double at 8% — within days of the exact 9.01-year answer, which is why the shortcut is trusted for rates roughly between 6% and 10%.

How this is calculated

The Rule of 72 is a mental-math shortcut for compound growth:

years to double ≈ 72 ÷ annual rate (as a percentage)

It approximates the exact doubling-time formula, ln(2) ÷ ln(1 + rate), which has no simple mental shortcut of its own. The two curves are closest together around an 8% rate — which is also why 72 (rather than 70 or 69, its more mathematically pure cousins) was chosen: it divides evenly by more small numbers, making the mental arithmetic easier.

The same relationship runs in reverse: dividing 72 by a target number of years gives the approximate rate needed to double money in that time — for example, doubling in 10 years takes roughly 7.2% a year.

When to use this calculator

Use this for a fast gut-check on any quoted return: '8% a year' becomes 'doubles in about 9 years' without reaching for a calculator, which is exactly the shortcut's purpose.

It is equally useful in reverse when you have a target: to double savings in 10 years needs roughly 7.2% a year, letting you judge quickly whether a goal is realistic for a given strategy.

Pair it with the exact doubling-time figure when precision matters — retirement projections or long compounding horizons are exactly where the Rule of 72's small approximation error can compound into a meaningfully different answer.

Common mistakes

Trusting the shortcut far outside its sweet spot — it stays accurate roughly between 6% and 10%, but drifts noticeably at very low or very high rates where the exact log formula should be used instead.
Entering the rate as a decimal (0.08) instead of a whole percentage (8) — the classic 72 ÷ rate formula expects the percentage number, not the fraction.
Applying it to a nominal rate without adjusting for inflation or fees — the doubling time it gives is for the rate you enter, not necessarily your real, after-cost return.

Frequently asked questions

What is the Rule of 72?: A mental-math shortcut for compound growth: divide 72 by the annual percentage rate to estimate the number of years an investment takes to double.
How accurate is the Rule of 72?: Very close for rates between about 6% and 10% (within a few weeks of the exact answer). Outside that band the approximation drifts further from the exact log-based doubling time.
What is the exact formula?: Exact doubling time = ln(2) ÷ ln(1 + r), where r is the rate as a decimal. This is the precise inverse of the compound-growth formula, with no approximation.
Can I use it to find the rate needed to double in N years?: Yes — rearrange to rate ≈ 72 ÷ years for a quick estimate, or use the exact form 2^(1/years) − 1 for the precise rate; doubling money in 10 years needs about 7.18% exactly, versus 7.2% from the shortcut.
Does the Rule of 72 work for tripling or quadrupling money?: Not directly — those use the Rule of 114 (triple) and Rule of 144 (quadruple) respectively, following the same ln(n)/ln(1+r) logic with n = 3 or 4 instead of 2.
Why does a higher rate reduce the shortcut's accuracy?: The Rule of 72 is a linear approximation to a logarithmic relationship; the two curves are closest together near 8% and diverge more the further the rate sits from that point in either direction.