Free · Doubling time · 72 ÷ rate
Rule of 72 calculator
The Rule of 72 estimates how long money doubles at a given return: years ≈ 72 ÷ rate. Works for stocks, savings, inflation, debt — any compounding rate.
Where Rule of 72 actually drifts · Snowballr exact-formula comparison vs 72/r approximation
Most accurate near 8% — error under 0.4 years
At 8% the rule gives 9.00 yrs vs exact 9.01 yrs. At 4% it overshoots by 0.3 yrs. At 20% it undershoots by 0.2 yrs. Below 2% and above 25%, switch to ln(2)/ln(1+r) for sub-month precision.
We pair the Rule of 72 estimate with the exact answer on every result so you can see the drift in real time instead of just trusting the shortcut.
Rule of 72 table: interest rate → years to double
| Interest rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 1% | 72.0 yrs | 69.7 yrs |
| 2% | 36.0 yrs | 35.0 yrs |
| 3% | 24.0 yrs | 23.4 yrs |
| 4% | 18.0 yrs | 17.7 yrs |
| 5% | 14.4 yrs | 14.2 yrs |
| 6% | 12.0 yrs | 11.9 yrs |
| 7% | 10.3 yrs | 10.2 yrs |
| 8% | 9.0 yrs | 9.0 yrs |
| 9% | 8.0 yrs | 8.0 yrs |
| 10% | 7.2 yrs | 7.3 yrs |
| 12% | 6.0 yrs | 6.1 yrs |
| 15% | 4.8 yrs | 5.0 yrs |
| 20% | 3.6 yrs | 3.8 yrs |
| 24% | 3.0 yrs | 3.2 yrs |
Rule of 72 is most accurate near 8% — exact at lower or higher rates drifts slightly.
Practical Rule of 72 uses
- Illustrative 10% nominal return: double every ~7.2 years. $10k → $20k → $40k → $80k by year 21.6.
- Illustrative 7% real return: purchasing power doubles in ~10.3 years; actual returns vary.
- Savings APY: enter the current quoted APY; the doubling estimate changes when the rate changes.
- Inflation: enter an assumed rate (3% would imply roughly 24 years); actual inflation varies by period and basket.
- Debt APR: enter the contract APR and account for payments and fees; unpaid debt at 22% would double in roughly 3.3 years under a constant-rate illustration.
Why Rule of 72 works
To double: (1+r)^t = 2
t = ln(2) / ln(1+r)
t ≈ 0.693 / r (for small r)
t ≈ 69.3 / rate%
72 is used instead of 69.3 because it's evenly divisible
by 1, 2, 3, 4, 6, 8, 9, 12 — convenient mental math.Rule of 72 Calculator FAQ
What is the Rule of 72?
A mental-math shortcut for estimating doubling time: years to double ≈ 72 ÷ annual return rate. At 8% return, money doubles every 9 years. At 6%, every 12 years. Works for any compounding rate, in either direction (investments doubling, inflation eroding).
How accurate is the Rule of 72?
About 1–2% from the exact result across rates around 4%–12%, with error increasing outside that range. For more precision: use ln(2) ÷ ln(1+r) = exact years to double.
Can I use the Rule of 72 for monthly compounding?
Use the effective annual rate. A 6% APR compounded monthly = 6.17% APY → ~11.7 years to double. If you use the nominal 6%, you'd get 12 years — close enough for mental math but the APY version is technically correct.
Does the Rule of 72 work for inflation?
Yes — and it's depressing. At 3% inflation, prices double in 24 years. At 4%, in 18 years. Same math, opposite direction: your $100 today buys what $50 buys in 24 years if inflation runs at 3%.
What's the Rule of 70 or Rule of 69?
Alternative approximations. Rule of 69 (or 69.3) is exact for continuous compounding. Rule of 70 is sometimes used for higher precision at moderate rates. Rule of 72 dominates because 72 has many factors — easier to divide mentally.
How do I use the Rule of 72 in real life?
Use the rate you actually have: divide an account's quoted APY, an assumed investment return, an inflation assumption or a debt APR into 72. For example, 8% gives about 9 years. The result is a shortcut for intuition; payments, fees, taxes and changing rates can materially change a real account.
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