This Rule of 72 calculator answers investing’s most famous mental math: divide 72 by your annual return to get the years money needs to double — with the exact logarithmic answer beside it, and tools to run the rule in every direction.
The rule also works in reverse on anything growing or shrinking exponentially — inflation at 3% halves purchasing power in ~24 years; a population growing 1% doubles in ~70.
Why 72 Works
The exact doubling time is ln(2) ÷ ln(1+r) — not mental math. The number 72 approximates it across the rates humans actually meet (2–12%) because ln(2) ≈ 69.3 gets a nudge upward by the compounding curvature, and 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12. Below 2% the “rule of 69.3” is tighter; above 15%, accuracy fades (at 20%: rule says 3.6 years, exact is 3.80). Within its home range the rule is off by under ~2% — the best trade of accuracy for memorability in all of finance. Projects with deposits need the full machinery of our Future Value Calculator. Part of our Finance Calculators collection.
The Table Everyone Quotes
| Return | Rule of 72 | Exact | Return | Rule of 72 | Exact |
|---|---|---|---|---|---|
| 2% | 36.0 yrs | 35.00 | 7% | 10.3 yrs | 10.24 |
| 3% | 24.0 yrs | 23.45 | 8% | 9.0 yrs | 9.01 |
| 4% | 18.0 yrs | 17.67 | 10% | 7.2 yrs | 7.27 |
| 5% | 14.4 yrs | 14.21 | 12% | 6.0 yrs | 6.12 |
| 6% | 12.0 yrs | 11.90 | 15% | 4.8 yrs | 4.96 |
Worked Examples (Verified)
- At 8%: the rule says 72 ÷ 8 = 9.0 years; the exact answer is 9.01 — as good as mental math gets
- At 6%: 12.0 vs exact 11.90 years
- Inflation at 4% halves your cash’s buying power in ~18 years — the rule pointed at your savings account is the most persuasive investing argument ever compressed into one division
- Credit-card debt at 24% APR doubles in 72 ÷ 24 = 3 years if unpaid — the rule has a dark side and this is it
Related Tools
- Future Value Calculator — exact projections with deposits
- Savings Goal Calculator — doubling with a deadline
- Finance Calculators — the full collection
Frequently Asked Questions
What is the Rule of 72?
A mental-math shortcut: years to double ≈ 72 ÷ annual return (%). At 8%, about 9 years; at 6%, 12 years. It also inverts — the return needed to double in N years ≈ 72 ÷ N percent.
How accurate is the Rule of 72?
Within about 2% for returns between 2% and 12% (9.0 predicted vs 9.01 exact at 8%). Errors grow outside that band: at 20% it predicts 3.6 years against a true 3.80.
Why 72 and not 69.3?
69.3 (= 100 × ln 2) is the continuous-compounding constant and wins below ~2%. For annual compounding at everyday rates, 72’s slight overshoot compensates the curve — and 72 is divisible by many small numbers, making the mental division trivial.
Does the rule work for inflation or population?
Yes — it applies to any exponential growth or decay: prices at 3% inflation double in ~24 years (purchasing power halves), a city growing 1.5% doubles in ~48 years, a decaying asset at −6%/yr halves in ~12.
How long does money take to triple?
The companion rule: 114 ÷ rate (the “Rule of 114”), and 144 ÷ rate to quadruple (two doublings). At 8%, tripling takes about 14.3 years by rule, 14.27 exactly.
Is this Rule of 72 calculator free?
Yes — free, instant, no sign-up.