🔵 Stokes’ Law Calculator
Enter the particle diameter, particle density, fluid density, and fluid viscosity to find the terminal settling velocity using Stokes’ Law.
What This Calculator Does
Stokes’ Law predicts the terminal (constant) settling velocity of a small, rigid, spherical particle falling or rising through a viscous fluid under gravity, once the drag force balances the net gravitational force.
The Formula
Stokes’ Law is v = (2/9) × ((ρp − ρf) × g × r²) ÷ μ, where v is terminal velocity, ρp is particle density, ρf is fluid density, g is gravitational acceleration (9.80665 m/s²), r is the particle’s radius, and μ is the fluid’s dynamic viscosity. A positive result means the particle sinks; a negative result means it rises (the particle is less dense than the fluid).
- Stokes’ Law is only accurate for laminar flow around the particle, generally when the particle Reynolds number is below about 1; this calculator also reports that Reynolds number so you can check validity.
- At higher Reynolds numbers, drag no longer follows Stokes’ linear relationship and more general drag-coefficient methods are needed.
This is the standard Stokes’ Law formula used for general physics, sedimentation, and educational reference purposes.