Cell Doubling Time Calculator
Find the cell doubling time and specific growth rate from a count over time.
3 doublings over 6 h · growth rate μ = 0.347 /h.
N(τ) = N₀ · 2^(τ ÷ Td): the count doubles every 2 h, so it climbs from 1,000 to 8,000 over 6 h.
Doubling time is Td = t · ln2 ÷ ln(N ÷ N₀), where N₀ is the starting count, N the final count, and t the elapsed time. A culture growing from 1,000 to 8,000 cells in 6 hours doubles log₂(8) = 3 times, so Td = 6 ÷ 3 = 2 hours, a growth rate μ of 0.347 /h.
What doubling time measures
During the exponential (log) phase of growth, a population multiplies by a fixed factor in each equal slice of time. The doubling time Td is how long it takes that population to double. Count the cells at two moments — an initial count N₀ and a later count N separated by an elapsed time t — and the number of doublings is log₂(N ÷ N₀). Dividing the elapsed time by the doublings gives the time per doubling. A shorter Td means faster growth: bacteria under ideal conditions can double in minutes, while mammalian cells take about a day.
Doublings = log₂(N ÷ N₀) = ln(N ÷ N₀) ÷ ln2. Specific growth rate μ = ln(N ÷ N₀) ÷ t.
Worked example
A bacterial culture grows from N₀ = 1,000 cells to N = 8,000 cells over t = 6 hours. How long does one doubling take?
- 1 Take the growth ratio N ÷ N₀. N ÷ N₀ = 8,000 ÷ 1,000 = 8. The population multiplied 8-fold over the interval.
- 2 Count the doublings with log₂. doublings = log₂(8) = ln(8) ÷ ln2 = 2.0794 ÷ 0.6931 = 3. The culture doubled three times.
- 3 Divide elapsed time by the doublings. Td = t ÷ doublings = 6 h ÷ 3 = 2 hours per doubling.
- 4 Optionally get the growth rate μ. μ = ln(N ÷ N₀) ÷ t = 2.0794 ÷ 6 ≈ 0.347 per hour — the continuous per-capita growth rate.
Typical doubling times
Approximate values under favourable lab conditions; real rates vary with medium, temperature, and strain.
| Cell type | Typical doubling time |
|---|---|
| Escherichia coli | ~20 minutes |
| Saccharomyces cerevisiae (baker’s yeast) | ~90 minutes |
| HeLa / typical mammalian cell line | ~24 hours |
How to read the result
This applies to the exponential phase only. Cultures grow exponentially just for a window: after a lag phase and before nutrients run out or waste builds up (the stationary phase). Pick your two counts inside that log phase, or the calculated Td will understate the true peak growth rate.
Growth rate versus doubling time. The specific growth rate μ = ln(N ÷ N₀) ÷ t and the doubling time are two views of the same thing, linked by Td = ln2 ÷ μ. A higher μ means a shorter Td. Growth rate is handy for continuous-culture math; doubling time is easier to picture at the bench.