Calculator
Pick a solving mode, select units, and compute. Advanced options include drag model, custom constants, and uncertainty propagation.
Tip: For water near room temperature, η ≈ 1.0 mPa·s. Nanoparticles often use an effective hydrodynamic radius larger than the core radius.
Example data table
| Fluid / Case | T (K) | η (mPa·s) | r | Estimated D (m²/s) |
|---|---|---|---|---|
| Water, small nanoparticle | 298 | 1.0 | 50 nm | 4.36e-12 |
| Water, micron-scale particle | 298 | 1.0 | 1 µm | 2.18e-13 |
| Glycerol-rich mixture (higher viscosity) | 298 | 100 | 100 nm | 2.18e-14 |
These are illustrative values using the no-slip drag factor (C = 6π).
Formula used
The Stokes–Einstein relationship connects diffusion to thermal energy and viscous drag for a spherical particle:
D = kB T / (C η r)
Where D is diffusion coefficient, kB is Boltzmann’s constant, T is absolute temperature, η is dynamic viscosity, r is particle radius, and C is the drag factor (commonly 6π for no-slip).
- No-slip boundary (standard): C = 6π
- Perfect slip (idealized): C = 4π
- Custom: Set C to match a specific hydrodynamic model.
How to use this calculator
- Select what you want to solve for (D, r, η, or T).
- Enter the known values and choose each unit.
- Pick the drag model (no-slip is typical for liquids).
- Optionally add percent uncertainties to propagate error.
- Click Compute to view results above the form.
- Use the download buttons to export CSV or PDF.
Note: The Stokes–Einstein relation is most reliable for spherical particles in continuum flow, away from extreme confinement, and when the effective hydrodynamic radius is well-defined.