Microbial Growth Curve Plotter
Plot the classic four-phase bacterial growth curve — lag, log (exponential), stationary, and death — from a starting population, lag duration, growth rate, carrying capacity, and death rate. Two 3D diagrams compare the lag phase (adapting, not yet dividing) to the log phase (rapid division), and charts trace population size through all four phases over time.
Reviewed by the ToolNestr Editorial Team — July 2026
Lag phase vs. log phase
1. Lag phase
Cells present but not yet dividing — adapting to the environment.
2. Log phase
Rapid, constant-rate division — the population is doubling repeatedly.
The full growth curve
How it works
The core idea in one line: a bacterial population's entire life story in a closed environment is written in just four acts — adapt, multiply freely, plateau against limits, then decline — and each act follows its own simple, predictable mathematical rule.
Lag phase: N(t) = N0
population stays flat while cells adapt, for 0 ≤ t < t_lag
Log phase: N(t) = N0·e^(k(t−t_lag))
exponential growth until reaching carrying capacity K
Stationary phase: N(t) = K
population plateaus at the carrying capacity
Death phase: N(t) = K·e^(−kd(t−t_death))
exponential decline once nutrients are exhausted
A batch bacterial culture moves through four distinct phases as its environment changes under it. During lag phase, cells synthesize what they need to grow but don't yet divide measurably. Once ready, they enter log phase, dividing at a constant exponential rate until nutrients start running low. As growth slows to match the death rate, the population plateaus at the environment's carrying capacity during stationary phase. Finally, once nutrients are exhausted and waste has accumulated further, cells die faster than new ones form, and the population declines through an exponential death phase — the same exponential math as growth, just running in reverse.
Worked example 1 — finding the log phase duration
Given: N0 = 1,000 cells, growth rate k = 0.693 per hour (≈1 hour doubling time), carrying capacity K = 1,024,000 cells (exactly 1,000 × 2¹⁰).
Choosing K as an exact power-of-2 multiple of N0 makes this example land on a clean 10-hour log phase — real cultures rarely divide such round numbers of times, but the math works identically either way.
Worked example 2 — the full four-phase timeline
Given: Using the same culture: lag phase = 2 hours, log phase = 10 hours (from example 1), stationary phase = 3 hours, then death phase begins with kd = 0.35 per hour.
Death phase decline follows the same exponential math as growth, just with population shrinking instead of expanding — a useful reminder that "exponential" describes the mathematical pattern, not automatically growth.
The four phases at a glance
Each phase reflects a different balance between cell division and cell death.
| Phase | What's happening | Population trend |
|---|---|---|
| Lag | Cells adapting, synthesizing enzymes | Flat |
| Log (exponential) ★ | Rapid, constant-rate division | Exponential increase |
| Stationary | Birth rate ≈ death rate, resources limiting | Flat (plateau) |
| Death | Death rate exceeds birth rate | Exponential decrease |
★ Reference row (worked example 1). The log phase is the only period where the growth rate constant k directly and predictably drives population change — the other three phases each reflect a different limiting factor taking over.
Where the microbial growth curve actually matters
🏭 Fermentation batch timing
Industrial fermentation processes are timed to harvest cells or products at the optimal phase — often late log or early stationary phase, depending on whether the target product accumulates during growth or afterward.
💊 Antibiotic testing timing
Antibiotic susceptibility testing is standardized to use log-phase cultures specifically, since actively dividing cells respond most predictably and consistently to antibiotic exposure.
🧫 Food spoilage and preservation
Understanding the full growth curve — including how long lag phase delays spoilage — informs food preservation techniques and shelf-life predictions for perishable products.
🔬 Microbiology education and research
The four-phase growth curve is one of the most fundamental concepts in microbiology, taught as the foundation for understanding how any closed microbial population behaves over time.
Common misconceptions
"Bacteria don't grow at all during the lag phase."
Cells are metabolically very active during lag phase, synthesizing new enzymes, RNA, and cellular machinery needed for growth in the new environment — they simply aren't yet dividing at a measurable rate.
"The stationary phase means all the bacteria have stopped dividing."
Cells are often still dividing during stationary phase — but at almost exactly the same rate that other cells are dying, so the net population size stays roughly constant even though individual cell turnover continues.
"Every bacterial culture eventually enters a death phase."
In a continuously fed environment (like a chemostat, or a natural ecosystem with ongoing nutrient input), a population can remain in a growth-death balance indefinitely without ever entering a true death phase — the classic four-phase curve specifically describes a closed batch culture with finite, non-renewed resources.
"The growth curve looks the same for every bacterial species and every environment."
The duration and steepness of each phase varies enormously depending on species, temperature, nutrient availability, and starting population — the four-phase shape is a general pattern, not a fixed, universal timeline.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Microbiology — Chapter 9, "Microbial Growth" (free, peer-reviewed). openstax.org
- • Madigan et al., Brock Biology of Microorganisms — The bacterial growth curve chapter.
- • Monod (1949) — foundational bacterial growth curve research, Annual Review of Microbiology.
Log phase: N=N0·e^(k(t−t_lag)); death phase: N=K·e^(−kd(t−t_death)). A simplified model — real growth curves can deviate from perfectly exponential math in each phase.
How to use this calculator
Enter starting parameters
Initial population, lag duration, log-phase growth rate, and carrying capacity.
Enter later-phase parameters
Stationary phase duration and the death-phase decline rate.
Read the full curve
All four phase transition times and the resulting growth curve plot automatically.
Related tools
Frequently asked questions
What are the four phases of bacterial growth?
Lag phase (cells adapt to the new environment, little growth), log/exponential phase (rapid, constant-rate division), stationary phase (growth stalls as resources deplete and waste accumulates), and death phase (cells die faster than new ones form).
Why does the lag phase happen at all?
Cells transferred to a new environment need time to synthesize the enzymes and cellular machinery required for growth in that specific environment before they can begin dividing rapidly — this adaptation period is the lag phase.
What ends the log phase and starts the stationary phase?
As nutrients become depleted and metabolic waste products accumulate, cells can no longer sustain their maximum division rate — growth slows and eventually plateaus as the birth rate equals the death rate, defining the stationary phase.
Is the stationary phase population size the same as the environment's carrying capacity?
Yes — the stationary phase population level is set by the environment's carrying capacity, the maximum population that available nutrients, space, and waste tolerance can support.
Why does the death phase happen?
Once nutrients are exhausted and toxic waste products build up further, the death rate exceeds any remaining reproduction rate, and the population size declines — often itself following an exponential decay pattern, just like the log phase's growth in reverse.