Stokes' law gives the drag force on a small sphere moving slowly through a viscous fluid: F_drag = 6πμrv. At terminal velocity this drag plus buoyancy equals gravity, giving v_t = 2r²(ρ_s − ρ_f)g / 9μ.

When is Stokes' law valid?

It is accurate when the Reynolds number Re = ρ_f · v · 2r / μ is below about 0.1, and still a useful approximation up to Re ≈ 1. Above Re ≈ 1, inertial effects dominate and you need the full drag equation instead.

What units should I use for viscosity?

Enter dynamic viscosity in mPa·s (millipascal-seconds), also called centipoise (cP). Water at 20 °C is about 1.002 mPa·s; honey is roughly 2000–10000 mPa·s; glycerol is about 1412 mPa·s at 20 °C.

What if the sphere is less dense than the fluid?

If ρ_s < ρ_f, the net buoyant force exceeds gravity and the sphere rises rather than falls. The calculator will display a note and show the upward terminal speed.

Does this account for wall effects?

No. Stokes' law assumes an infinite fluid domain. Near container walls the actual velocity is lower. Apply a Ladyzhenskaya or Faxén correction if your vessel diameter is close to the sphere diameter.

Terminal Velocity in Fluid

Name: Terminal Velocity in Fluid
Availability: InStock
Author: Nham Vu

Enter sphere radius, density, and fluid viscosity to calculate terminal velocity using Stokes' law for viscous flow.

Sphere & Fluid Parameters

Quick Presets

Sphere radius (mm)

Sphere density (kg/m³)

Fluid density (kg/m³)

Dynamic viscosity (mPa·s)

Water ≈ 1.002 mPa·s · Glycerol ≈ 1412 mPa·s · Honey ≈ 2000–10 000 mPa·s

Enter parameters and click Calculate to see results.

Summary

Enter sphere radius, density, and fluid viscosity to calculate terminal velocity using Stokes' law for viscous flow.

How it works

Enter the sphere radius in millimeters.
Enter the sphere density (e.g. 2500 kg/m³ for quartz sand).
Enter the fluid density (e.g. 1000 kg/m³ for water).
Enter the dynamic viscosity of the fluid in mPa·s (millipascal-seconds); water at 20 °C is about 1.002 mPa·s.
Click Calculate — the tool applies Stokes' law and returns terminal velocity in m/s, cm/s, and mm/s.
The Reynolds number is shown so you can judge whether Stokes' law is valid (Re < 0.1 is ideal; Re < 1 is still a good approximation).

Use cases

Predict sedimentation rate of particles in water or other liquids.
Solve fluid mechanics and physics lab problems on Stokes' law.
Estimate blood cell settling velocity in clinical hematology context.
Analyze oil droplet fall rates in Millikan-experiment scenarios.
Model sand or silt settling in environmental engineering.
Compare terminal speeds across particle sizes or fluid viscosities.
Verify hand calculations for viscous drag coursework.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu