Doubling Time Calculator
Find out how many periods it takes for a quantity to double at a given growth rate. This calculator gives you the exact result alongside the popular Rule of 70 and Rule of 72 approximations.
Doubling time tells you how long exponential growth takes to double a value. Whether you are tracking population, investments, bacteria, or inflation, the concept is the same.
Exact Formulas:
For continuous compounding: t = ln(2) / r
For discrete compounding (once per period): t = ln(2) / ln(1 + r)
Where r is the growth rate as a decimal (e.g., 7% = 0.07) and ln is the natural logarithm.
The Rule of 70:
A quick mental shortcut: Doubling Time is about 70 / (growth rate in percent). At 7% growth, something doubles in roughly 70 / 7 = 10 periods. This works best for rates between 2% and 10%.
The Rule of 72:
Similar to the Rule of 70 but uses 72 instead. It is slightly less accurate overall but easier to compute mentally because 72 has more factors (divisible by 2, 3, 4, 6, 8, 9, 12). At 6% growth: 72 / 6 = 12 periods.
Real-World Examples:
- A savings account at 3% interest doubles in about 23.4 years
- A population growing at 2% per year doubles in about 35 years
- An investment earning 10% annually doubles in roughly 7.3 years