Diffusion Coefficient Calculator

A diffusion coefficient (D) is a measure of how quickly a dissolved substance spreads through a solvent by random thermal motion. It has units of area per time, m2/s in SI, and appears directly in Fick's first and second laws of diffusion, which describe how a concentration gradient drives net movement of a solute.

The Stokes-Einstein equation, D = kT / (6 pi eta r), gives the diffusion coefficient of a spherical solute in a liquid, where k is the Boltzmann constant, T is absolute temperature, eta is the solvent's dynamic viscosity, and r is the solute's effective (hydrodynamic) radius. It connects a molecule's size directly to how fast it diffuses.

For a glucose molecule with an effective radius around 0.36 nm in water at 25 degrees C (viscosity 0.89 mPa.s), the Stokes-Einstein relation gives a diffusion coefficient of about 682 um2/s, close to the experimentally measured value of roughly 600 to 670 um2/s for glucose in dilute aqueous solution.

D is inversely proportional to the solute's radius r, so a molecule twice as large diffuses at half the rate under the same conditions. Small ions and simple molecules, typically 0.1 to 0.5 nm in radius, diffuse far faster than large organic molecules or polymers of the same chemical family.

Two effects both push D higher as temperature rises, the T term directly in the numerator increases, and the solvent's viscosity eta typically drops at higher temperature, and since eta is in the denominator, a lower viscosity further increases D. Both effects act in the same direction, which is why diffusion-limited processes speed up noticeably with heating.

Millipascal-seconds (mPa.s), numerically identical to centipoise (cP), the traditional viscosity unit in reference tables. Water at room temperature has a viscosity close to 1 mPa.s. Other common solvents differ: ethanol is around 1.07 mPa.s at 25 degrees C, while glycerol is roughly 950 mPa.s, over a thousand times more viscous than water.

Both use the identical Stokes-Einstein formula, D = kT / (6 pi eta r). This chemistry version is scoped and sliders are sized for small solutes and ions, roughly 0.05 to 2 nm, the scale relevant to general chemistry, environmental chemistry, and lab diffusion problems. The Biophysics version is sized for the much larger 0.5 to 50 nm range typical of globular proteins, nucleic acids, and virus particles.

In SI units (m2/s), typical small-molecule diffusion coefficients fall between roughly 1e-9 and 1e-10, because diffusion over the meter-scale unit happens extremely slowly at the molecular level. This calculator also reports D in um2/s and cm2/s, both easier to read for lab-scale comparisons.

The hydrodynamic radius is the radius of an idealized hard sphere that would diffuse at the same rate as the actual solute, including any bound solvent shell. For small, roughly spherical molecules like glucose or sucrose it tracks closely with the molecule's physical size; for ions it is typically larger than the bare ionic radius because of tightly bound water molecules (hydration shell).

No, not directly. The Stokes-Einstein equation specifically models a solute diffusing through a continuous liquid solvent. Diffusion of one gas through another gas follows a different framework, based on kinetic theory and mean free path, closely related to the physics behind the Ideal Gas Law rather than viscous drag through a liquid.

Common laboratory methods include the diaphragm cell (measuring concentration change across a porous barrier over time), dynamic light scattering, and NMR pulsed-field gradient techniques, all of which infer D from how quickly a solute spreads out or how its signal changes as concentration gradients relax toward equilibrium.