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Stokes' Law Settling Velocity Calculator

Calculate the terminal settling velocity of a small spherical particle falling through a viscous fluid using Stokes' law, v = (2/9)·(ρp−ρf)·g·r²/μ, plus the particle Reynolds number that checks whether the law's low-Reynolds-number assumption actually holds.

Settling (terminal) velocity
0.001362 m/s
Particle Reynolds number
0.0681
Validity check
Stokes' law applies cleanly

How it works

Stokes' law gives the constant speed a small sphere settles at once viscous drag exactly balances the net downward force of gravity minus buoyancy: v = (2/9) × (ρp − ρf) × g × r² ÷ μ, where r is the particle's radius, ρp and ρf are the particle's and fluid's densities, g is gravitational acceleration, and μ is the fluid's dynamic viscosity. The r² term means settling speed is extremely sensitive to size — a particle twice as wide settles four times as fast.

This is a different physical regime from this site's existing Terminal Velocity calculator, which uses the quadratic drag equation for macroscopic falling objects at high Reynolds number. Stokes' law instead governs small particles — silt, dust, emulsion droplets — where viscous forces dominate over the fluid's inertia, which is exactly why it's the basis of lab sedimentation and particle-size settling tests.

Because the formula's derivation assumes smooth, laminar flow around the particle, it only holds when the particle Reynolds number Re = ρf·v·d ÷ μ stays well below 1 — this is computed and reported alongside the velocity, rather than silently assumed, since a result for a particle outside that regime would be numerically returned but physically wrong.

FAQ

What happens if my particle Reynolds number comes back above 1?

It means the particle is too large, too dense relative to the fluid, or the fluid too thin for Stokes' law's laminar-flow assumption to hold — the actual settling velocity will be lower than this formula predicts, because turbulent drag (which Stokes' law ignores) starts to matter. In that regime, a drag-equation model like this site's Terminal Velocity calculator, which accounts for a drag coefficient at higher Reynolds numbers, is the more accurate tool.

Why are density and viscosity not affected by the metric/imperial toggle?

kg/m³ for density and Pa·s for viscosity are already the standard units used worldwide in fluid mechanics regardless of which unit system the rest of a calculation uses, the same convention this site's Buoyancy and Hagen-Poiseuille Flow calculators already follow — only the particle's diameter and gravity, genuine physical measurements people do express differently in different unit systems, get the page's toggle.

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