Bacterial Growth Calculator
Work out how many cells a culture reaches after a given time from its doubling time — exponential growth — and how many generations that is.
How fast a population doubles into a big number.
How the bacterial growth calculator works
In the exponential phase a bacterial population doubles every generation time: N = N₀ × 2^(t ÷ t_d). E. coli doubles every 20 minutes in rich medium, so one cell becomes over a million in seven hours. The calculator also gives the growth rate constant and the time to reach a target count in Detailed mode.
Formula: N = N₀ × 2^(t ÷ t_d) · generations = t ÷ t_d
Worked examples
| Inputs | Cells after the time | Note |
|---|---|---|
| 1,000 cells, 20-min doubling, 4 hours | 4,096,000 | 12 generations → 4.1 million |
| 1 cell, 20 min, 7 hours | 2,097,152 | 2 million from one cell |
| 500 cells, 60-min doubling, 24 hours | 8,388,608,000 | 8.4 billion |
FAQFrequently asked questions
Does growth really stay exponential?
Only while nutrients last and waste is low — the log phase. Cultures then slow (stationary phase) as the model stops applying.
What is E. coli's doubling time?
About 20 minutes in rich broth at 37 °C; much slower on minimal media or at lower temperatures. Other bacteria range from 10 minutes to days.
How is the growth-rate constant related?
k = ln 2 ÷ doubling time; the population follows N₀ e^(kt).
How long to go from 1 to a billion cells?
log₂(10⁹) ≈ 29.9 generations — ten hours at a 20-minute doubling time.
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- National Institute of Standards and Technology — the US measurement and reference-data authority
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.