Diffusion Coefficient Calculator

°C
Temperature in Celsius; converted to Kelvin internally.
mPa·s
Water at 25°C: 0.89 mPa·s.
nm
Radius of the diffusing particle in nanometers.
Chemistry

Estimate the diffusion coefficient of a spherical molecule in solution using the Stokes-Einstein equation.

Formula

D = k_B × T / (6π × η × r)
  • k_B = 1.381×10⁻²³ J/K (Boltzmann constant).
  • Temperature in Kelvin = °C + 273.15.
  • Viscosity converted from mPa·s to Pa·s (÷1000).
  • Particle radius converted from nm to m (÷10⁹).

1 nm radius particle in water at 25°C

Inputs
  • Temperature: 25 °C
  • Solvent Viscosity: 0.89 mPa·s
  • Hydrodynamic Radius: 1 nm

D = (1.381×10⁻²³ × 298.15) / (6π × 8.9×10⁻⁴ × 10⁻⁹) ≈ 2.46×10⁻¹⁰ m²/s.

Frequently asked questions

What are the units of diffusion coefficient?
m²/s in SI units; cm²/s is also common. For gases, values are ~10⁻⁵ m²/s; for liquids ~10⁻⁹ m²/s.
What is the Stokes-Einstein equation valid for?
Spherical particles much larger than solvent molecules in a homogeneous solvent.