Diffusion Coefficient Calculator

The Stokes-Einstein relation gives how fast particles diffuse in a fluid.

How the Math Works

The Stokes-Einstein formula calculates diffusion coefficient (D) by relating it to fundamental physical properties of a particle and its environment. The equation D = kB·T ÷ (6π·η·r) shows that diffusion increases with higher temperature (T) and decreases with greater fluid viscosity (η) or particle radius (r). Boltzmann's constant (kB) acts as a proportionality factor linking thermal energy to molecular motion. This model assumes spherical particles in a continuous fluid, where Brownian motion dominates and interactions are negligible beyond viscous drag.

Practical Applications

This calculation is essential in fields like chemistry, biology, and materials science to predict how substances spread in liquids or gases. For example, pharmaceutical researchers use it to estimate drug molecule movement in bodily fluids, optimizing delivery systems. Environmental scientists apply it to model pollutant dispersion in water or soil. Industrial engineers rely on D values to design efficient mixing processes or assess contaminant transport in groundwater remediation projects.

Day-to-Day Use

While not something you calculate daily, this principle explains everyday phenomena. It helps us understand how flavors and preservatives disperse in food and beverages, why medications dissolve at different rates in your body, and how pollutants spread through air or water before settling. Even in skincare, diffusion coefficients inform how active ingredients penetrate creams, making this formula indirectly relevant to personal health and environmental safety.

Worked example

1 nm particle in water at 298 K → ~2.5 × 10⁻¹⁰ m²/s.

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