Thiele Modulus Calculator

Thiele Modulus Formula

Worked Example

A 2 mm radius immobilised-enzyme bead with k = 0.5 per s and Dₑ = 10⁻⁹ m²/s:

1. φ = (R/3)√(k/Dₑ) = 14.90711985 (characteristic length V/A = R/3)
2. η = (1/φ)[1/tanh(3φ) − 1/(3φ)] = 0.06558203932

Regime: strongly diffusion-limited (η ≈ 1/φ)

GATE tip

Using V/A as the length (R/3 for a sphere) makes all shapes give η ≈ 1/φ at large φ, so answers for different geometries can be compared directly.

More Enzyme and Microbial Kinetics Calculators

• 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.

  Open the michaelis-menten 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 →

• 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 →

• 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 →

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.