Rule of 72 & Doubling Time Calculator
Rule of 72 calculator: exact years for money to double at a given return, compared with the rule-of-72 estimate.
t = ln 2ln(1 + r) ≈ 72r %
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Money doubles after t = ln 2 ÷ ln(1 + r) years. The rule of 72 approximates this as 72 ÷ the rate in percent and is accurate for rates between about 4 % and 12 %.
It also works for inflation: at 3 % inflation prices double in about 24 years.
Estimates for information only, not financial advice.
Formula
t = ln 2ln(1 + r) ≈ 72r %
| Symbol | Quantity | Units |
|---|---|---|
| r | Annual return | %, × |
| t | Years to double | years, months |
Worked example
Given: r = 8 %
t = ln 2ln(1 + r)
Result: t = 9.00647 years
Frequently asked questions
How long does money take to double at 8 %?
Exactly 9.01 years; the rule of 72 gives 72 ÷ 8 = 9.