Diffusion Coefficient Calculator
The diffusion coefficient of a molecule or particle in a liquid from its size, the temperature and the viscosity — the Stokes–Einstein equation — with how long it takes to diffuse a micrometre or a millimetre.
A particle in a liquid is jostled by thermal motion and slowed by viscous drag: D = k_B T ÷ (6π η r).
How the diffusion coefficient calculator works
A particle in a liquid is jostled by thermal motion and slowed by viscous drag: D = k_B T ÷ (6π η r). Small molecules in water at room temperature diffuse at about 10⁻⁹ m²/s; proteins ten times slower; a micron bead a thousand times slower. Diffusion covers distance with the square root of time — a micrometre in a millisecond, a millimetre in a quarter of an hour, a metre in decades — which is why cells are small and stirring exists.
Formula: D = k_B T ÷ (6π η r); t = x² ÷ (2D)
Worked examples
| Inputs | Diffusion coefficient (m²/s) | Note |
|---|---|---|
| Lysozyme (1.9 nm) in water at 25 °C | 1.291e-10 | 1.29 × 10⁻¹⁰ m²/s |
| Glucose (0.36 nm) at 25 °C | 6.816e-10 | 6.8 × 10⁻¹⁰ m²/s |
| A 50 nm virus at 37 °C | 6.585e-12 | 6.6 × 10⁻¹² m²/s |
FAQFrequently asked questions
What radius do I use for a protein?
The hydrodynamic radius, a little larger than the physical one because of bound water: roughly 0.9 nm for a 10 kDa protein, 1.9 nm for lysozyme (14 kDa), 3.5 nm for serum albumin (66 kDa). It scales with the cube root of mass for globular proteins.
Why does distance go with the square root of time?
Diffusion is a random walk: steps in random directions cancel, so the net displacement grows only as √(2Dt). Doubling the distance takes four times as long — small scales are fast, large scales hopeless.
Does Stokes–Einstein work for small molecules?
Approximately. It assumes a sphere much larger than the solvent molecules; for something glucose-sized it is within a factor of two, which is still useful.
How does temperature change it?
Directly through T, and more through viscosity: water at 37 °C is 20% less viscous than at 25 °C, so D rises about 25% between the two.
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- CSIRO — Australia's national science agency
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.