Doubling Time Formula
Calculate how long it takes a population to double in size.
Works for bacteria, investments, and any exponential growth.
The Formula
t_d = ln(2) / r ≈ 0.693 / r
Doubling time tells you how long it takes for a quantity growing exponentially to double. It works for populations, money, bacteria, or anything with a constant growth rate.
Variables
| Symbol | Meaning |
|---|---|
| t_d | Doubling time (same units as the growth rate) |
| ln(2) | Natural logarithm of 2 (approximately 0.693) |
| r | Growth rate (as a decimal, per unit time) |
Example 1
A bacterial culture grows at 4% per hour. How long until it doubles?
r = 0.04 per hour
t_d = 0.693 / 0.04
t_d ≈ 17.3 hours
Example 2
A city's population grows at 2.5% per year. When will it double?
r = 0.025 per year
t_d = 0.693 / 0.025
t_d ≈ 27.7 years
When to Use It
Use the doubling time formula when:
- Estimating how fast a population will grow
- Planning for resource needs based on growth projections
- Comparing growth rates of different organisms or investments
- Understanding the impact of small changes in growth rate