Rule of 72 Calculator
Estimate how long it takes for your investment to double using the Rule of 72 — compares Rule of 72, Rule of 69.3, and exact logarithmic formulas with a full growth-multiple table.
Rule of 72 Calculator
Calculator Settings
Quick Reference
Calculation Results
Doubling Time (Rule of 72)
9 years
72 / 8 = 9.00
Exact Doubling Time
9 years
ln(2) / ln(1 + 0.08) = 9.0065
Approximation Error
-0.07%
Rule of 72 vs exact formula
Investment Growth
$10,000 → $20,000
in ~9 years
Triple (3x)
14 yr 3 mo
Quadruple (4x)
18 years
Growth Multiple Table
| Multiple | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2x | 9.00 yr | 9.01 yr | -0.07% |
| 3x | 14.26 yr | 14.27 yr | -0.07% |
| 4x | 18.00 yr | 18.01 yr | -0.07% |
| 5x | 20.90 yr | 20.91 yr | -0.07% |
| 6x | 23.26 yr | 23.28 yr | -0.07% |
| 7x | 25.27 yr | 25.28 yr | -0.07% |
| 8x | 27.00 yr | 27.02 yr | -0.07% |
Complete Guide to the Rule of 72
What Is the Rule of 72?
The Rule of 72 is a simple mental-math shortcut that tells you how many years it takes for an investment to double in value at a fixed annual compound interest rate. You divide 72 by the annual rate and get a surprisingly accurate estimate — no logarithms required.
It works because 72 is close to the natural-log constant needed for doubling (ln 2 ≈ 0.693) and has many convenient divisors (2, 3, 4, 6, 8, 9, 12), making head-math easy. The rule is most accurate for rates between 4% and 20% and was first described by the Italian mathematician Luca Pacioli in 1494.
For related compound-growth tools, try our Compound Interest Calculator or Investment Calculator with Inflation.
The Formula
Rule of 72 (approximate):
Years to Double ≈ 72 / Annual Interest Rate (%)
Example: at 8% → 72 / 8 = 9 years
Exact formula (logarithmic):
Years to Double = ln(2) / ln(1 + r)
Where: r = annual rate as a decimal (e.g. 0.08 for 8%). At 8% → ln(2) / ln(1.08) ≈ 9.006 years
Variants: Rule of 69.3 and Rule of 70
Rule of 69.3 uses ln(2) × 100 ≈ 69.3 as the numerator. It is mathematically closer for continuous compounding but harder to divide in your head.
Rule of 70 splits the difference — easier mental math than 69.3, slightly more accurate than 72 at low rates. Many economists and textbooks prefer 70 for GDP and inflation estimates.
Use our SIP Calculator to see how regular monthly contributions accelerate doubling even further.
Benefits of Using the Rule of 72
Quick Mental Math
Evaluate investment opportunities on the spot without a calculator or spreadsheet
Compare Rates Instantly
Quickly see that 6% doubles in 12 years while 12% doubles in 6 — doubling the rate halves the time
Understand Inflation Impact
At 3% inflation your cost of living doubles in 24 years — the same rule works in reverse
Set Realistic Goals
Know how many doubling periods you need to turn $10K into $80K (three doublings at your rate)
Tips for Using the Rule of 72
Use it for debt too: Credit card debt at 24% APR doubles in just 3 years if unpaid. Check our Debt Payoff Calculator for a payoff plan.
Adjust for taxes and fees: Use your after-tax return, not the gross rate. A 10% return with 25% tax is effectively 7.5% — doubling in 9.6 years, not 7.2.
Chain doublings for big multiples: To go from $10K to $80K you need 3 doublings (10→20→40→80). At 8% that is 3 × 9 = 27 years.
Common Mistakes
Using the Nominal Rate Instead of Real Rate
If your investment earns 8% but inflation is 3%, your real doubling time is 72 / 5 = 14.4 years, not 9. Always subtract inflation for purchasing-power calculations.
Applying It to Variable Returns
The Rule of 72 assumes a fixed rate. Stock market returns fluctuate year to year — the rule gives a rough guide using the average, but volatility drag means the actual doubling time is longer.
Trusting It at Extreme Rates
Below 2% or above 30% the error grows beyond 5%. At 1% the Rule of 72 says 72 years but the exact answer is 69.7 — a 3.3% error. For extreme rates, use the exact ln(2)/ln(1+r) formula.
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OpenFrequently Asked Questions
What is the Rule of 72?
A quick mental shortcut: years to double your money ≈ 72 ÷ annual interest rate. At 6% returns, money doubles in ~12 years. At 9%, ~8 years. At 12%, ~6 years. It's an approximation that works best for rates 4–15%; gets less accurate at extremes.
Where does the number 72 come from?
The exact doubling formula uses ln(2) / ln(1+r). For small rates, ln(1+r) ≈ r and ln(2) ≈ 0.693. So years to double ≈ 0.693 / r. Multiply both sides by 100 (to use rate as a percent): years ≈ 69.3 / rate %. Rule of 72 rounds up because 72 has more divisors (2, 3, 4, 6, 8, 9, 12) for easier mental math.
What's the Rule of 69.3?
More mathematically accurate version using continuous compounding: years to double = 69.3 / rate %. Closer to exact for very low rates (1–4%). The calculator shows you all three estimators (72, 69.3, exact ln formula) so you can see the small differences.
Does the Rule of 72 work for inflation?
Yes — same math, opposite direction. Years for prices to DOUBLE at given inflation rate ≈ 72 ÷ inflation rate. At 3% inflation, prices double every ~24 years. At 6%, every ~12 years. The 'rule of 72 inflation' is just the regular rule applied to a destructive force instead of a constructive one.
Can I use the Rule of 72 for tripling?
Use Rule of ~115 for tripling and ~144 for quadrupling. These derive from ln(3)/ln(1+r) and ln(4)/ln(1+r) the same way. For a more general rule: years to multiply N times = 72 × log₂(N) / rate %. The calculator shows the full growth-multiple table for any rate you enter.
When does the Rule of 72 break down?
At very low rates (under 2%) and very high rates (above 30%) the approximation drifts. For low rates, the Rule of 70 (ln(2)/r ≈ 0.693/r) is more accurate. For high rates, just use the exact formula: years = ln(2) / ln(1 + r). The calculator handles the math precisely regardless of input rate.