Schmidt Number Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The Schmidt number is calculated with Sc = ν ÷ D, where ν is the fluid's kinematic viscosity and D the mass diffusivity of the species diffusing within it. For water vapor diffusing in air, the Schmidt number is about 0.6, a classic reference value in fluid mechanics.
Explanation
The Schmidt number is the mass-transfer analogue of our Prandtl number calculator in heat transfer: where the Prandtl number compares momentum diffusion to heat diffusion, the Schmidt number compares it to the diffusion of a chemical species (such as water vapor, a pollutant, or a solute) within a carrier fluid. A Schmidt number close to 1 means momentum and matter diffuse at comparable rates in the fluid; a number well above 1 (typical of liquids, where mass diffusion is very slow compared to viscosity) means matter diffuses much more slowly than momentum is transmitted. This number comes up directly in the study of drying, evaporation, the dispersion of pollutants in the atmosphere or in water, and more generally in any situation where mass transfer by diffusion must be characterized and compared to the flow of the carrier fluid — a role for mass transfer comparable to that of the Reynolds number for characterizing a flow's regime.
Example: water vapor diffusing in air
Inputs
Air's kinematic viscosity: 1.5×10⁻⁵ m²/s. Water vapor's mass diffusivity in air: 2.5×10⁻⁵ m²/s.
Calculation
Sc = (1.5×10⁻⁵) ÷ (2.5×10⁻⁵) = 0.6.
Result
This Schmidt number of 0.6 is the classic reference value cited for water vapor in air.
Frequently asked questions
Why does the Schmidt number of air and water differ so much by species?
Mass diffusivity D strongly depends on the nature of the diffusing species and the medium it moves through: it's generally much larger in a gas than in a liquid, where the solute's molecules are much closer together and therefore move with greater difficulty. That's why typical Schmidt numbers for liquids (often several hundred to several thousand) are much higher than for gases (generally close to 1).
What is the relationship between the Schmidt number and the Prandtl number?
The two numbers share exactly the same mathematical structure (a ratio between kinematic viscosity and another diffusivity), but apply to different phenomena: the Prandtl number compares momentum diffusion to thermal diffusion, while the Schmidt number compares it to mass diffusion. A third number, the Lewis number, directly relates these two diffusivities (thermal and mass) to each other (Le = Sc ÷ Pr), without going through viscosity.
In which practical fields is this number used?
The Schmidt number is central in chemical engineering (designing absorption columns and dryers), environmental science (modeling pollutant dispersion in air or water), and biology (diffusion of nutrients or dissolved gases in an aqueous medium) — anywhere the speed at which a substance spreads by diffusion within a moving fluid needs to be characterized.