Diffusion Coefficient Calculator

How Diffusion Coefficient Calculator Works?

The Diffusion Coefficient Calculator estimates the translational diffusion coefficient of a spherical molecule or particle moving through a fluid. It uses the Stokes–Einstein relationship, which connects Brownian motion with absolute temperature, dynamic viscosity, and particle radius.

In this equation, $D_t$ is the translational diffusion coefficient, $k_B$ is the Boltzmann constant, $T$ is absolute temperature, $\eta$ is dynamic viscosity, and $r$ is the particle radius. The calculator uses $k_B=1.380649\times {10}^{-23}$ J/K.

Diffusion increases with temperature because thermal motion becomes stronger. It decreases as viscosity increases because the fluid produces greater resistance to movement. It also decreases as particle radius increases, meaning smaller molecules and particles generally diffuse more rapidly than larger ones under the same conditions.

For example, using 298.15 K, a dynamic viscosity of 0.001 Pa·s, and a particle radius of 1 nm gives a diffusion coefficient of approximately 2.18 × 10⁻¹⁰ m²/s. The calculator reports the result in the available square-length-per-second output forms.

Practical Use Cases

Physical chemists can estimate how quickly small molecules move through liquids and use the result when interpreting molecular transport, reaction environments, and solution behavior.

Biochemists and pharmaceutical researchers can approximate the diffusivity of proteins, drug molecules, vesicles, or other biological particles in fluid media, helping assess mixing, molecular encounters, and delivery processes.

Colloid and nanoparticle researchers can use the calculator to relate particle size and solvent viscosity to Brownian motion, including expected mobility in microscopy and suspension studies.

Microscopy and single-particle tracking users can compare measured particle trajectories with the theoretical diffusion coefficient and identify whether observed motion is broadly consistent with thermal diffusion.

Chemical and process engineers can obtain an initial transport estimate for species moving through liquid systems, supporting preliminary mass-transfer, dispersion, and fluid-transport analysis.

Students and laboratory educators can investigate how changing temperature, viscosity, or radius affects molecular motion while applying the Stokes–Einstein relationship to realistic examples.

Accuracy and Limitations

The calculator is mathematically accurate for the Stokes–Einstein model when the particle is approximately spherical, suspended in a homogeneous Newtonian fluid, sufficiently separated from boundaries and other particles, and moving under ordinary no-slip hydrodynamic conditions. It assumes the supplied radius is the particle radius rather than its diameter and treats the entered viscosity and temperature as representative of the entire sample. Results may be unreliable for concentrated suspensions, non-Newtonian or structured fluids, particles near surfaces, non-spherical or flexible objects, very small solutes where continuum hydrodynamics becomes questionable, or systems with convection, sedimentation, binding, or active transport. The numerical precision of the result is also limited by the precision and validity of the temperature, viscosity, and radius values entered.

Quick Examples