GROWTH

Free Online Microbial Growth Curve & Doubling Time Calculator

Step 2 of 5: Isolate exponential growth phase, calculate generation doubling time $t_d$, specific growth rate $\mu_{max}$, and fit Modified Gompertz equations. • 100% Free & Open Access.

100% FREE STEP 2 OF 5 • FERMENTATION WORKFLOW
EXPERIMENTAL DATA & PRESETS INPUT
Industrial Host Preset
Kinetic Model Formulation
Time (h), Optical Density (OD₆₀₀) 11 points
MICROBIAL GROWTH DYNAMICS & FITTED TRAJECTORY CANVAS VISUALIZER
Y-Axis Scale:
● Converged (SSE = 0.043)
FERMENTATION HANDOFF ➔ STEP 3
Calculated maximum growth rate μ_max = 0.58 h⁻¹ and lag phase λ = 2.15 h ready to feed into Multi-Model Kinetic Parameter Fitting (Step 3) to resolve half-saturation $K_s$ and substrate inhibition $K_i$.
GROWTH PHASE DIAGNOSTICS METRICS
Carrying Capacity (A / OD_max)
6.95 OD
Stationary phase plateau asymptote
Exponential Phase Window
4.0 h ➔ 12.0 h
Duration: 8.0 hours of uninhibited growth
Specific Division Rate (k)
0.84 gen/h
Generations per hour ($k = \mu / \ln 2$)
Total Biomass Accumulation
86.3× Fold
6.43 net population doublings
Max Acceleration Point (t_infl)
7.85 h
Inflection point of maximum slope
📊 Computed Results & Analytical Outputs LIVE CALCULATION
Max Growth Rate (μ_max)
0.582 h⁻¹
Specific rate in exponential phase
Doubling Time (t_d)
71.4 min
1.19 hours per division
Lag Phase Duration (λ)
2.15 h
Physiological adaptation period
Regression Quality (R²)
0.9984
RMSE: 0.064 • Gompertz fit

📚 Microbial Growth Curve, Specific Growth Rate (μ) & Doubling Time Guide Fermentation Kinetics • Step 1 of 5

Theoretical Principles & Engineering Fundamentals

Microbial batch cultures exhibit five characteristic phases: lag phase, exponential (log) growth phase, deceleration phase, stationary phase, and death phase. Accurately extracting specific growth rate ($\mu$, hr⁻¹) and generation doubling time ($t_d$, hr) during the true exponential phase is essential for metabolic flux analysis and seed train scheduling.

Governing Equations & Mathematical Formulations

Specific Growth Rate (μ) \mu = \frac{\ln(X_2) - \ln(X_1)}{t_2 - t_1}
Logarithmic slope of biomass expansion during unimpeded exponential growth.
Generation Doubling Time t_d = \frac{\ln(2)}{\mu} \approx \frac{0.693}{\mu}
Time required for culture biomass or cell population to double in magnitude.
Exponential Biomass Trajectory X(t) = X_0 \times e^{\mu \times t}
Fundamental exponential growth equation governing active microbial division.

Industrial Benchmark Data & Parameter Reference

OrganismMax Specific Growth Rate μ_max (hr⁻¹)Doubling Time td (min)Optimal Temperature (°C)
Escherichia coli0.60 – 1.2020 – 70 min37.0°C
Bacillus subtilis0.50 – 0.9045 – 80 min37.0°C
Saccharomyces cerevisiae0.35 – 0.4590 – 120 min30.0°C
CHO Cell Culture0.025 – 0.04018 – 28 hours36.5°C

Frequently Asked Questions (Bioprocess Engineering FAQ)

How do I know which data points belong to the true exponential phase?
Plot $\ln( ext{OD}_{600})$ versus time. The linear region with the highest coefficient of determination ($R^2 > 0.99$) defines the uninhibited exponential growth phase.
Why does the lag phase occur?
Inoculated cells must adjust to the new osmotic, nutrient, and temperature environment by synthesizing enzymes, ribosomes, and cofactors before active cell division can commence.
What triggers the transition to stationary phase?
Stationary phase is triggered by exhaustion of the limiting carbon or energy source, dissolved oxygen depletion, or accumulation of toxic organic acids and metabolic byproducts.