How to Use the Doubling Time Calculator
The doubling time calculator determines how many periods it takes for a quantity to double given a constant percentage growth rate. Enter your percent increase per period to find the doubling time.
Formula
The doubling time formula is:
$$
t_d = \frac{\ln(2)}{\ln(1 + r)}
$$
Where:
- $$t_d$$ = doubling time (in periods)
- $$r$$ = growth rate per period (as a decimal)
This formula is derived from the compound growth equation $$A = P(1 + r)^t$$, where we solve for the time $$t$$ when $$A = 2P$$.
Example Calculation
For a 7% growth rate per period:
- Growth rate $$r = 0.07$$
- $$\ln(2) \approx 0.6931$$
- $$\ln(1.07) \approx 0.0677$$
- Doubling time = $$\frac{0.6931}{0.0677} \approx 10.24$$ periods
So with 7% growth per period, your quantity will double in approximately 10.24 periods.
The Rule of 72
A quick approximation for doubling time is the Rule of 72:
$$
t_d \approx \frac{72}{\text{percentage rate}}
$$
For 7% growth: $$72 \div 7 \approx 10.29$$ periods, which is very close to the exact calculation.