How to Use This Calculator
- Enter an annual growth rate — an investment return, GDP growth, a population growth rate, or an inflation rate.
- Pick a rule variant. 72 is the classic choice; 70 and 69.3 are slightly more accurate for low or continuously compounded rates.
- Optionally set a starting value and a time horizon to see a real projection.
- Read the results: the approximate doubling time from the rule, the exact doubling time, how many times the amount doubles over your horizon, and the projected ending value. The chart shows the exponential curve.
The Formula Explained
The Rule of 72 is a shortcut for the doubling time of anything that grows at a compound rate:
The exact answer comes from solving (1 + r)ᵗ = 2 for t:
- ratePercent — the growth rate written as a number, e.g. 8 for 8%
- r — the same rate as a decimal, e.g. 0.08
Related shortcuts: divide 114 by the rate to estimate a tripling, and 144 for a quadrupling.
Frequently Asked Questions
How accurate is the Rule of 72?
Between roughly 6% and 10% — the range most investors care about — it is usually within a few weeks to a couple of months of the exact doubling time. It drifts slightly at very low or very high rates, which is why the exact figure is shown alongside it.
When should I use 70 or 69.3 instead of 72?
The mathematically exact base for continuous compounding is 100 × ln(2) ≈ 69.3. Use 69.3 or 70 for continuously compounded or lower rates. 72 endures because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the mental arithmetic easy.
Can the Rule of 72 be used for inflation?
Yes. Divide 72 by the inflation rate to estimate how long until prices double — equivalently, until a fixed sum of money loses half its purchasing power. At 3% inflation that is about 24 years.
Related Calculators
- Compound Interest — the full growth curve with contributions.
- Inflation Calculator — apply the doubling idea to rising prices.
- Retirement / 401(k) — see how many doublings fit before you retire.