Chemistry
Diffusion Coefficient Calculator
Find how fast a particle spreads through a fluid using the Stokes-Einstein relation.
Your inputs
Change any value to update the result instantly.
Diffusion coefficient D
245.3731 µm²/s
In SI units
2.4537 x 10^-10 m²/s
Friction coefficient used
1.6776 x 10^-11 kg/s
Time to diffuse 1 µm
0.0007 s
Model
Stokes-Einstein, spherical particle in a continuous fluid
Stokes-Einstein assumes a hard sphere much larger than the solvent molecules, no charge effects and dilute conditions. Water at 25 °C has a viscosity near 0.00089 Pa·s.
What this calculator does
Calculates a diffusion coefficient from temperature and friction, either directly or through the Stokes-Einstein relation.
What your result means
How quickly a particle spreads through the fluid by random thermal motion.
Formula and working
D = k_B·T / ξ, with ξ = 6πηr for a sphere
- 1
Collect the inputs
Temperature = 298.15 K; Friction input = 1; Fluid viscosity η = 0.0009 Pa·s; Particle radius r = 1 nm; Friction coefficient ξ = 0 kg/s
- 2
Apply the formula
D = k_B·T / ξ, with ξ = 6πηr for a sphere
- 3
Result
Diffusion coefficient D = 245.3731 µm²/s
Frequently asked questions
Symbols and assumptions
- D
- Diffusion coefficient
- k_B
- Boltzmann constant
- η
- Viscosity
- r
- Particle radius
- • Spherical particle much larger than the solvent molecules.
- • Dilute solution with no charge interactions.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • Crowded, charged or non-spherical systems deviate substantially.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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