Stokes Drag Calculator
Stokes' law describes the viscous resistance felt by a small sphere moving slowly through a fluid, where the flow stays smooth and laminar. It is the foundation of sedimentation analysis, aerosol science, the falling-ball viscometer and Millikan's oil-drop experiment. This calculator takes the fluid dynamic viscosity, the sphere radius and its speed, then returns the drag force in newtons and millinewtons. It is accurate only at very low Reynolds number, below about 1, where inertial effects are negligible compared with viscous ones.
Stokes' law formula
F = 6 * pi * mu * r * v
mu = dynamic viscosity (Pa*s)
r = sphere radius (m)
v = speed relative to fluid (m/s)
The drag force opposes motion and is proportional to viscosity, radius and speed. The result is given in newtons and millinewtons. Stokes drag is the dominant resistance for tiny slow-moving particles.
Viscous drag context
- Stokes' law holds only at Reynolds number below about 1, where flow is fully laminar.
- Drag grows linearly with speed, unlike high-speed drag which grows with the square of speed.
- Dynamic viscosity of water at 20 degrees Celsius is approximately 0.001 pascal-seconds.
- The falling-ball viscometer uses Stokes' law in reverse to measure fluid viscosity.
- Millikan measured the charge of the electron by balancing Stokes drag against gravity and an electric field.
Stokes drag: frequently asked questions
What is Stokes' law?
Stokes' law gives the viscous drag force on a small smooth sphere moving slowly through a viscous fluid: F = 6 * pi * mu * r * v, where mu is the dynamic viscosity, r is the sphere radius and v is its speed relative to the fluid. The force opposes motion and grows linearly with speed.
When is Stokes' law valid?
It is valid at very low Reynolds number, below about 1, where flow around the sphere is smooth and laminar with no separation or wake. This covers tiny particles, droplets and microorganisms in liquids, or fine dust settling in air. At higher speeds inertial drag dominates and the law no longer holds.
How does drag depend on radius and speed?
Stokes drag is directly proportional to both radius and speed, so doubling either doubles the force. This is unlike high-speed drag, which grows with the square of speed and the square of radius. The linear dependence is what makes very small particles settle so slowly in a fluid.
What viscosity value should I enter?
Dynamic viscosity is a property of the fluid and temperature. Water at 20 degrees Celsius is about 0.001 pascal-seconds and air is about 0.0000181. Because it is empirical and temperature dependent, viscosity ships here as a user-editable input so you can match your fluid and conditions.
How is Stokes' law used to find terminal velocity?
When a sphere falls under gravity, it reaches terminal velocity when drag balances net weight. Setting Stokes drag equal to the buoyant weight gives v = 2 * (rho_p - rho_f) * g * r^2 / (9 * mu). This is the basis of sedimentation analysis and the falling-ball viscometer.
Official sources
- NASA Glenn Research Center: Drag of a sphere.
- U.S. National Institute of Standards and Technology: Fluid Metrology.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.