Diffusion Coefficient Calculator

A diffusion coefficient describes how rapidly particles spread through random thermal motion. Larger coefficients indicate faster dispersal, while smaller values indicate slower movement through the surrounding medium. This calculator uses the Stokes-Einstein equation, D = kBT divided by 6πηr, where kB is the Boltzmann constant, T is absolute temperature, η is dynamic viscosity, and r is the hydrodynamic radius of a spherical particle. With all quantities converted to SI units, the result is expressed in square metres per second. The equation captures three useful trends. Raising temperature increases thermal energy and therefore increases diffusion. Increasing viscosity creates more drag and reduces diffusion. Increasing particle radius also reduces diffusion because a larger particle experiences greater hydrodynamic resistance. These relationships make the equation valuable for estimating molecular transport, comparing nanoparticles, planning dynamic light scattering experiments, and checking mass-transfer calculations. Use absolute temperature in kelvin rather than degrees Celsius. Dynamic viscosity must be entered in pascal-seconds; one millipascal-second equals 0.001 pascal-seconds. The calculator accepts radius in nanometres and converts it to metres internally. Be careful not to enter diameter in place of radius, because doing so doubles the denominator and halves the reported coefficient. The hydrodynamic radius may also differ from a dry geometric radius when a molecule carries a solvation shell or adopts a non-spherical conformation. Stokes-Einstein assumes a dilute suspension of spherical particles moving through a continuous Newtonian fluid with no-slip boundary conditions. It works best when the particle is substantially larger than individual solvent molecules and interactions between particles are weak. Crowded solutions, porous particles, highly anisotropic molecules, non-Newtonian fluids, interfaces, and extremely small solutes can depart from these assumptions. Measured viscosity at the actual temperature is preferable because viscosity can change sharply even over a modest temperature interval. Treat the result as an ideal estimate suitable for comparison and experiment planning. For high-precision work, use the solvent's temperature-dependent viscosity, an experimentally determined hydrodynamic radius, and any correction required by the measurement geometry. Diffusion coefficients are often reported in square centimetres per second; multiply the result in square metres per second by 10,000 to make that conversion. Always record temperature and solvent conditions alongside a reported diffusion coefficient so another researcher can interpret or reproduce it.