Monod Equation Calculator
A culture with μmax = 0.5 per hour and Ks = 0.2 g/L grows at 0.416667 per h when the substrate is 1 g/L, doubling in about 1.7 hours.
0.416666666666667 per h
Full answer, then cut to fewer decimals (not rounded):
- 0.416666666666667 per h
- 0.41666666666666 per h
- 0.4166666666666 per h
- 0.416666666666 per h
- 0.41666666666 per h
- 0.4166666666 per h
- 0.416666666 per h
- 0.41666666 per h
- 0.4166666 per h
- 0.416666 per h
- 0.41666 per h
- 0.4166 per h
- 0.416 per h
- 0.41 per h
- 0.4 per h
- Fraction of μmax
- 83.33333333 %
- Doubling time ln 2/μ
- 1.663553233 h
Step-by-step solution
- μ = μmax S ÷ (Ks + S) = 0.5 × 1 ÷ (0.2 + 1)
- μ = 0.4166666667 per h
Monod Equation Formula
μ = μmax S / (Ks + S)
Ks the substrate concentration at μ = μmax/2; doubling time ln 2/μ
Worked Example
A culture with μmax = 0.5 per hour and Ks = 0.2 g/L at S = 1 g/L:
- μ = μmax S ÷ (Ks + S) = 0.5 × 1 ÷ (0.2 + 1)
- μ = 0.4166666667 per h
Doubling time ln 2/μ: 1.663553233 h
GATE tip
In a chemostat at steady state μ = D, so the residual substrate S = Ks D/(μmax − D) follows directly from the Monod equation.
More Enzyme and Microbial Kinetics Calculators
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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.
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Microbial Growth Calculator
N = N₀ e^(μt), t_d = ln 2 / μ
generations n = log₂(N/N₀)
Example: A culture growing from 1000 to 64,000 cells in 6 hours: Specific growth rate μ = 0.693147 per h.
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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.
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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
Is Monod the same as Michaelis–Menten?
The form is identical, but Monod is empirical, describing growth of whole cells, while Michaelis–Menten derives from enzyme mechanism.
When does Monod fail?
With substrate inhibition at high S (Andrews/Haldane model) or product inhibition, and in the lag and death phases.
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). Monod Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/monod-equation-calculator/
IEEE
Scientific Converters, "Monod Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/monod-equation-calculator/