Two counts and the time between them give the doubling time
You need the starting count N0, the later count Nt, and the time t between them. The ratio Nt/N0 is how many fold the culture grew; ln 2 (about 0.693) turns that into a count of doublings. The answer comes out in whatever time unit you put in — minutes for bacteria, hours for mammalian cells.
Number of doublings, if you want the intermediate step
A 10 fold rise is log2(10) = 3.32 doublings; an 8 fold rise is exactly 3. If a culture went from 2×10⁵ to 1.6×10⁶ cells (an 8 fold rise) over 72 hours, that is 3 doublings, so Td = 72 ÷ 3 = 24 hours.
Typical doubling times
| Cell or organism | Doubling time |
|---|---|
| E. coli (lab, rich medium) | ~20 min |
| Yeast (S. cerevisiae) | 60–90 min |
| CHO (Chinese hamster ovary) | 16–20 h |
| Vero (monkey kidney) | 24–30 h |
| HEK293 (human kidney) | 24–36 h |
| Primary fibroblasts | 18–24 h |
A doubling time that drifts well outside these ranges is a warning sign — overgrowth, contamination, a medium or temperature problem, or cells past their useful passage number.
What to hold steady
- Log phase only. Measure while the count is climbing exponentially, not during the initial lag or once cells crowd toward confluence.
- Same units, same log. Keep one time unit throughout. Natural log and log base 10 both work in the formula as long as you use the same base top and bottom.
- Related but distinct. The specific growth rate μ connects directly: Td = ln 2 ÷ μ = 0.693 ÷ μ.
Common questions
What is the doubling time formula?
Doubling time equals the elapsed time multiplied by the natural log of 2, divided by the natural log of the final count over the starting count. In symbols, Td = t times ln(2) divided by ln(Nt divided by N0).
Why do I get a negative or infinite doubling time?
A negative result means the final count is below the starting count, so the population shrank rather than grew. An infinite or undefined result means the two counts are equal. Doubling time is only defined while the culture is actually growing.
Should I measure during the exponential phase?
Yes. The formula assumes steady exponential growth, which only holds in the log phase. Readings taken during the lag phase at the start or the plateau near confluence give a doubling time that is too long and not representative.
