Michaelis-Menten Calculator

Michaelis-Menten Formula

Worked Example

An enzyme with Vmax = 100 and Km = 2 at [S] = 5:

1. v = Vmax[S] ÷ (Km + [S]) = 100 × 5 ÷ (2 + 5)
2. v = 71.42857143

[S] for v = ½Vmax (apparent Km): 2

GATE tip

At [S] = Km the rate is exactly Vmax/2; at [S] = 9Km it is 90 % of Vmax. These two facts solve many questions without a calculator.

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.

  Open the monod equation calculator →

• 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.

  Open the thiele modulus calculator →

• 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.

  Open the microbial growth calculator →

• 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.

  Open the chemostat calculator →

Frequently asked questions

Sources

• The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.