Stokes–Einstein diffusion coefficient from temperature, solvent viscosity and particle radius, plus root-mean-square displacement.
Result
How to use this tool
Enter temperature in °C or K.
Enter solvent viscosity in mPa·s (water at 25°C is 0.89).
Enter radius in nm or µm.
Read D in m²/s and µm²/s plus RMS displacement.
Formula & worked example
A 1 nm particle in water (0.89 mPa·s) at 25°C has D ≈ 2.45 × 10⁻¹⁰ m²/s (about 245 µm²/s).
Limitations — read this before you rely on it
Spherical-particle continuum approximation; not valid for molecules, rods, crowded or gel environments.
Frequently asked questions
D = k_B T / (6πηr): diffusion rises with temperature and falls with viscosity and particle size.
About 0.89 mPa·s at 25°C and 1.00 mPa·s at 20°C; the default here is water at 25°C.
The typical distance a particle wanders by diffusion in a given time, growing with the square root of time.
For particles near solvent-molecule size, non-spherical shapes, crowded solutions or non-Newtonian fluids.
m²/s is the SI unit; µm²/s is the practical unit for nanoparticles and cells.