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Diffusion Coefficient Calculator (Stokes-Einstein Equation)

Calculate the translational diffusion coefficient (D) of spherical particles in a viscous fluid medium.

Input Parameters

Instant Real-time Calculation

Temperature (Kelvin)

Dynamic Viscosity (η in mPa·s or cP; Water = 0.89 mPa·s at 25°C)

Particle Hydrodynamic Radius (r in nm)

Result Chemistry

Diffusion Coefficient (D)

-- × 10⁻⁹ m²/s

Export calculation:

Calculation Logic:

Calculates thermal Brownian motion diffusion rates of molecules through viscous fluids using the Stokes-Einstein relation.

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Understanding Diffusion Coefficient Calculator (Stokes-Einstein Equation) & Formula

Mathematical Formula: D = (k_B × T) / (6 × π × η × r); k_B = 1.380649 × 10⁻²³ J/K

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Diffusion Coefficients in Water at 25°C

Molecules / Particle	Hydrodynamic Radius	Diffusion Coeff D (m²/s)	Diffusion Time across 10 µm Cell
Water Molecule (Self-diff)	~0.15 nm	2.3 × 10⁻⁹ m²/s	~0.02 seconds
Glucose	~0.44 nm	6.7 × 10⁻¹⁰ m²/s	~0.07 seconds
Lysozyme (Protein)	~1.9 nm	1.1 × 10⁻¹⁰ m²/s	~0.45 seconds
BSA (Bovine Albumin)	~3.5 nm	6.0 × 10⁻¹¹ m²/s	~0.83 seconds
Ribosome (Macromolecule)	~10 nm	2.0 × 10⁻¹¹ m²/s	~2.5 seconds

How to Use the Diffusion Coefficient Calculator (Stokes-Einstein Equation)

1 Input fluid temperature in Kelvin.
2 Input solvent dynamic viscosity in mPa·s (centipoise).
3 Input particle hydrodynamic radius in nanometers (nm).
4 Read diffusion coefficient D.

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