Stokes Law Calculator - Viscous Drag & Terminal Velocity Solver
Use this Stokes Law Calculator to find viscous drag force, terminal velocity, or dynamic viscosity. Preset fluids for water, air, glycerol, and oil included.
Stokes Law Configuration
Calculation Results
What is a Stokes Law Calculator?
A Stokes Law Calculator is an essential fluid dynamics tool used by engineers, chemists, and students to quickly determine the viscous drag force acting on a sphere moving through a fluid, or to find the terminal settling velocity of a particle falling under gravity. Stokes' Law describes the simplest non-trivial case of fluid resistance: a rigid, smooth sphere in slow, laminar flow.
Common use cases for Stokes' Law calculations include:
- Calculating the settling velocity of sediment particles in water treatment and geological sedimentation studies.
- Determining the drag force on small droplets, bubbles, or pollen grains in air or other fluids.
- Solving for the unknown dynamic viscosity of a fluid when the drag force, radius, and velocity are measured.
- Analyzing pharmaceutical powder settling, food processing particle dynamics, and microfluidic device design.
To check whether your flow regime is even suitable for Stokes' Law, explore our Reynolds Number Calculator to confirm Re << 1 before trusting the result.
How Stokes Law Calculations Work
Stokes' Law describes the drag force on a sphere in laminar (creeping) flow. The drag force is directly proportional to the fluid's dynamic viscosity, the sphere's radius, and its velocity, with the proportionality constant 6π. When gravity drives the motion, balancing gravitational, buoyant, and drag forces yields the terminal velocity equation.
Each equation assumes the sphere is far from any walls and that inertial forces are negligible compared to viscous forces — the creeping flow regime where the Reynolds number is much less than 1.
According to Wikipedia — Stokes' Law, the drag force on a sphere in laminar flow is F = 6πμrv and the resulting terminal velocity is v_t = (2/9)(r²g(ρ_p − ρ_f))/μ.
For comparison with high-Reynolds-number drag, explore our Drag Equation Calculator to compute the drag force in turbulent regimes.
Key Concepts Explained
Dynamic Viscosity (μ)
A measure of a fluid's internal resistance to flow, expressed in pascal-seconds (Pa·s). Higher viscosity means thicker fluids and larger drag forces.
Laminar vs. Turbulent Flow
Stokes' Law applies only in laminar flow, characterized by a Reynolds number (Re) much less than 1. Beyond Re ≈ 1, wake formation and turbulence make the equation inaccurate.
Terminal Velocity
The constant speed reached when gravitational force is balanced by buoyancy and viscous drag. It represents the steady-state falling speed of the sphere.
Creeping Flow Regime
The low-Reynolds-number regime where inertial forces are negligible compared to viscous forces — the strict validity domain of Stokes' Law.
Use our Reynolds Number Calculator to verify the flow regime for any sphere–fluid combination.
How to Use This Calculator
Choose Solve Mode
Pick what to solve for: drag force, terminal velocity, or viscosity.
Select Fluid Preset
Choose water, air, glycerol, SAE 30 oil, or Custom to enter your own values.
Enter Sphere Radius
Type the radius of the spherical particle in metres (or cm in CGS).
Enter Velocity & Density
Set the velocity (for drag) or particle density (for terminal velocity).
View Results
Read the primary result, Reynolds number, and validity check instantly.
For solid sphere mass and density inputs, explore our Sphere Density Calculator to convert between mass, radius, and density.
Benefits of Using This Calculator
- • Solves Any Stokes Variable: Drag force, terminal velocity, or viscosity from a single universal interface.
- • Preset Fluid Library: NIST-traceable values for water, air, glycerol, and SAE 30 oil at 20°C instantly available.
- • Built-in Validity Check: Automatically computes the Reynolds number and warns you when Stokes' Law is outside its validity range.
- • Metric and CGS Units: Switch between SI (N, Pa·s, m/s) and CGS (dyne, poise, cm/s) for any textbook or lab.
For fluid property lookups including air density at altitude, explore our Air Density Calculator to set the right ρ_f for atmospheric problems.
Factors That Affect Your Results
Fluid Viscosity (μ)
Viscosity has a direct linear effect on drag force and an inverse linear effect on terminal velocity — doubling viscosity halves the settling speed.
Sphere Radius (r)
Radius has a linear effect on drag force and a squared effect on terminal velocity — a particle twice as large falls four times faster under Stokes flow.
Density Difference (ρ_p − ρ_f)
The greater the difference between particle density and fluid density, the higher the terminal velocity. Neutral buoyancy (ρ_p = ρ_f) means zero settling.
Reynolds Number Compliance
Beyond Re ≈ 1, the drag coefficient is no longer proportional to velocity, and Stokes' Law systematically under-predicts drag — switch to a turbulent drag model.
As derived in Bird, Stewart & Lightfoot — Transport Phenomena, Stokes' Law applies only in the creeping flow regime where the Reynolds number is much less than 1.
For density conversions and material property lookups, explore our Specific Gravity Calculator to find the right ρ_p for your particle.
Frequently Asked Questions (FAQ)
Q: What is Stokes Law in fluid mechanics?
A: Stokes' Law is the equation for the viscous drag force on a sphere moving slowly through a fluid. It states that F = 6πμrv, where F is the drag force, μ is the fluid's dynamic viscosity, r is the sphere's radius, and v is its velocity. The law only holds in laminar creeping flow, where the Reynolds number is much less than 1.
Q: How do you calculate Stokes drag force?
A: To calculate Stokes drag force, multiply 6π by the fluid's dynamic viscosity (μ in Pa·s), the sphere's radius (r in m), and the velocity (v in m/s). The result is the drag force in newtons opposing the sphere's motion. This formula assumes laminar flow and a rigid, smooth sphere.
Q: What is the formula for terminal velocity using Stokes Law?
A: The Stokes terminal velocity formula is v_t = (2/9) · (r²g(ρ_p − ρ_f)) / μ, where r is the sphere radius, g is gravitational acceleration (9.81 m/s²), ρ_p is particle density, ρ_f is fluid density, and μ is dynamic viscosity. This gives the steady-state settling speed of a sphere falling through a viscous fluid.
Q: When is Stokes Law valid (Reynolds number limit)?
A: Stokes' Law is valid only when the Reynolds number Re = (2ρ_f v r) / μ is much less than 1 — typically Re < 0.1 for accurate results. Above Re ≈ 1, flow separation and wake formation make the drag coefficient higher than 6πμrv, so a turbulent drag model should be used instead.
Q: How does viscosity affect the drag force on a sphere?
A: Viscosity has a direct linear effect on Stokes drag force. Doubling a fluid's dynamic viscosity doubles the drag force on a sphere moving at the same speed. This is why tiny particles settle slowly in water but quickly in air — air's viscosity is roughly 55 times lower than water's at 20°C.