Diffusion Coefficient Calculator
Enter the absolute temperature, the fluid's dynamic viscosity, and the particle's hydrodynamic radius. The calculator applies the Stokes-Einstein equation to estimate the diffusion coefficient, in m²/s.
Last updated: September 26, 2026
Frequently asked questions
What is the Stokes-Einstein equation?
It relates a spherical particle's diffusion coefficient to temperature, the fluid's viscosity, and the particle's radius: D = kB·T / (6πμr). It comes from combining Einstein's relation for Brownian motion with Stokes' drag law for a sphere.
Why does the calculator convert Celsius to kelvin?
The equation needs absolute temperature, since it reflects the average thermal energy of the particles (proportional to kBT). Using Celsius directly would give an incorrect result.
What is the hydrodynamic radius?
It's the effective radius of a sphere that would diffuse at the same rate as the actual particle, including any bound solvent or non-spherical shape effects folded into a single number. For a compact, roughly spherical molecule, it's close to its physical radius.
When does this equation work well?
Best for particles significantly larger than the surrounding solvent molecules, like proteins, viruses, or colloidal particles, in a fluid that behaves as a continuum around them.
When is it less accurate?
For small molecules comparable in size to the solvent, or in complex or non-Newtonian fluids, the continuum and spherical-particle assumptions break down and the equation becomes less reliable.
What units does the result use?
The diffusion coefficient comes out in m²/s using SI inputs (kelvin, Pa·s, meters). The calculator also shows the equivalent value in cm²/s, a unit you'll often see in the literature.