Stokes' Law Calculator — Terminal Settling Velocity
Enter the particle radius, particle density, fluid density and fluid dynamic viscosity to compute the terminal settling velocity and Stokes drag force for a small sphere moving through a viscous fluid.
µm
kg/m³
kg/m³
Pa·s
Particle sinks (ρₚ > ρ_f)
8.971 mm/s
settling velocity- 1
Convert radius to metres
r = 50 µm × 10⁻⁶ = 0.00005 - 2
Density difference Δρ = ρ_p − ρ_f
2,650 − 1,000 kg/m³ = 1,650 - 3
Terminal velocity (m/s)
(2÷9) × (0.00005)² × 1,650 × 9.80665 ÷ 0.001002 = 0.0089715v_t = 2r²(ρ_p − ρ_f)g / (9η) — positive = sinks, negative = rises. - 4
Convert to mm/s
0.0089715 m/s × 1000 = 8.9715
How does this calculator work?
Stokes' law gives terminal velocity as v_t = 2r²(ρ_p − ρ_f)g / (9η) and drag force as F_d = 6πηrv_t. Enter particle radius (µm), densities (kg/m³) and fluid viscosity (Pa·s). Valid for Reynolds number Re ≪ 1 (creeping flow). Typical use: fine particles settling in water or air.
Formula
How this is calculated
Stokes' law describes the drag force on a rigid sphere moving slowly through a viscous Newtonian fluid at low Reynolds number. When a particle sinks (or rises) through a fluid, three forces act on it: gravity (downward), buoyancy (upward) and drag (opposing motion). At terminal velocity these forces balance, giving v_t = (2/9) × r² × (ρ_p − ρ_f) × g / η, where r is particle radius, ρ_p and ρ_f are particle and fluid densities, g = 9.807 m/s² and η is the dynamic viscosity of the fluid.
The drag force at terminal velocity is F_d = 6π η r |v_t|, which equals the net (buoyancy-corrected) weight of the particle. The Reynolds number Re = ρ_f × |v_t| × 2r / η checks whether the creeping-flow assumption holds: Stokes' law is accurate for Re ≲ 0.1 and gives results within about 5 % up to Re ≈ 1. For larger, faster or denser particles (Re > 1) the formula underestimates drag and the Schiller-Naumann or turbulent-drag corrections should be applied.
Common applications include sedimentation of clay/silt in water (r ~ 1–10 µm), centrifugation of biological cells, aerosol particle dynamics in air and quality control of fine powders. Pre-loaded defaults correspond to a 50 µm quartz grain settling in water at 20 °C.
Frequently asked questions
Stokes' law is used to calculate the terminal velocity at which small spherical particles settle (or rise) in a viscous fluid. It is fundamental in sedimentology, chemical engineering, food science (cream rising in milk), medical diagnostics (sedimentation rate) and particle size analysis.
Stokes' law assumes creeping (laminar) flow, which requires the Reynolds number Re = ρ_f × |v_t| × 2r / η to be much less than 1. When Re exceeds 1, inertial effects become significant and the formula underestimates drag, making the terminal velocity overestimated. For Re > 1 use a corrected drag coefficient model.
When ρ_p < ρ_f the net gravitational force is upward — the particle rises rather than sinks (e.g. a bubble in liquid). The calculator returns a positive speed and labels it as rising. Examples include air bubbles in water and oil droplets in denser liquids.
Also known as
TG we-Calculate Editorial Team. (2026). Stokes' Law Calculator — Terminal Settling Velocity [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/stokes-law-calculator
TG we-Calculate Editorial Team. "Stokes' Law Calculator — Terminal Settling Velocity." TG we-Calculate. 2026. https://we-calculate.com/calculator/stokes-law-calculator.
TG we-Calculate Editorial Team, "Stokes' Law Calculator — Terminal Settling Velocity," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/stokes-law-calculator
@misc{wecalculate_stokes_law_calculator, title = {Stokes' Law Calculator — Terminal Settling Velocity}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/stokes-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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