Microbial Growth Calculator
A culture growing from 1000 to 64,000 cells in 6 hours has a specific growth rate of 0.693147 per h: six generations, one doubling per hour.
0.693147180559945 per h
Full answer, then cut to fewer decimals (not rounded):
- 0.693147180559945 per h
- 0.69314718055994 per h
- 0.6931471805599 per h
- 0.693147180559 per h
- 0.69314718055 per h
- 0.6931471805 per h
- 0.693147180 per h
- 0.69314718 per h
- 0.6931471 per h
- 0.693147 per h
- 0.69314 per h
- 0.6931 per h
- 0.693 per h
- 0.69 per h
- 0.6 per h
- Doubling (generation) time ln 2/μ
- 1 h
- Number of generations log₂(N/N₀)
- 6
- Growth rate constant (doublings per h)
- 1
Step-by-step solution
- μ = ln(N/N₀) ÷ t = ln(64) ÷ 6 = 0.6931471806 per h
- t_d = ln 2 ÷ μ = 1 h
Microbial Growth Formula
N = N₀ e^(μt), t_d = ln 2 / μ
generations n = log₂(N/N₀)
Worked Example
A culture growing from 1000 to 64,000 cells in 6 hours:
- μ = ln(N/N₀) ÷ t = ln(64) ÷ 6 = 0.6931471806 per h
- t_d = ln 2 ÷ μ = 1 h
Number of generations log₂(N/N₀): 6 · Growth rate constant (doublings per h): 1
GATE tip
Use counts from the exponential phase only. If a question gives log₁₀ counts, μ = 2.303 × Δlog₁₀N / Δt.
More Enzyme and Microbial Kinetics Calculators
-
Monod Equation Calculator
μ = μmax S / (Ks + S)
Ks the substrate concentration at μ = μmax/2; doubling time ln 2/μ
Example: A culture with μmax = 0.5 per hour and Ks = 0.2 g/L at S = 1 g/L: Specific growth rate μ = 0.416667 per h.
-
Chemostat Calculator
D = F/V = μ, S = Ks D/(μmax − D), X = Y(S₀ − S)
washout above D_crit = μmax S₀/(Ks + S₀); productivity DX
Example: A 2 L chemostat fed 0.5 L/h with 10 g/L substrate, μmax 0.5 per h, Ks 0.2 g/L, Y = 0.5: Steady-state biomass X = 4.9 g/L.
-
Michaelis-Menten Calculator
v = Vmax[S] / (Km + [S])
competitive: Km × (1 + [I]/Kᵢ); uncompetitive: Km and Vmax ÷ (1 + [I]/Kᵢ); non-competitive: Vmax ÷ (1 + [I]/Kᵢ)
Example: An enzyme with Vmax = 100 and Km = 2 at [S] = 5: Reaction rate v = 71.4286.
-
Thiele Modulus Calculator
Sphere: φ = (R/3)√(k/Dₑ), η = (1/φ)[1/tanh 3φ − 1/(3φ)]
slab: φ = L√(k/Dₑ), η = tanh φ / φ
Example: A 2 mm radius immobilised-enzyme bead with k = 0.5 per s and Dₑ = 10⁻⁹ m²/s: Effectiveness factor η = 0.065582.
Frequently asked questions
How fast can bacteria divide?
E. coli doubles about every 20 minutes in rich medium at 37 °C; Mycobacterium tuberculosis takes about 18–24 hours.
Can I use optical density?
Yes, during exponential growth OD is proportional to cell mass, so two OD readings give μ in the same way.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Microbial Growth Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/microbial-growth-calculator/
IEEE
Scientific Converters, "Microbial Growth Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/microbial-growth-calculator/