Stokes' Law Calculator

Stokes' law describes the viscous drag on a small sphere moving slowly through a Newtonian fluid. The drag force equals six pi multiplied by dynamic viscosity, sphere radius, and relative velocity. When a denser particle settles at terminal velocity, downward effective weight is balanced by upward buoyancy and viscous drag. Solving that balance gives terminal velocity as two times radius squared times the density difference times gravitational acceleration, divided by nine times dynamic viscosity. This calculator assumes a rigid, smooth, isolated sphere in an unbounded, motionless fluid. It uses standard gravitational acceleration of 9.80665 metres per second squared. Particle radius has a squared effect, so doubling radius makes the predicted settling velocity four times greater when every other property stays constant. A larger density difference promotes settling, while greater viscosity slows it. If the particle is less dense than the fluid, it rises rather than settles; this interface focuses on downward settling and therefore requires particle density to exceed fluid density. Stokes' formula applies in the creeping-flow regime, where inertia is negligible compared with viscous forces. Reynolds number provides an important check. Here it is calculated from fluid density, sphere diameter, terminal velocity, and viscosity. Values well below one support the assumption; values approaching or exceeding one indicate that inertial corrections may be important. The first example can intentionally illustrate a result outside the strict creeping-flow regime, reminding users not to accept the velocity without checking Reynolds number. Nearby walls, neighboring particles, non-spherical shapes, turbulence, fluid motion, slip, concentration effects, and non-Newtonian behavior can all alter settling. Very small particles may also be influenced by Brownian motion, while droplets and bubbles can circulate internally and require other drag relations. Stokes settling is widely used in sedimentation, particle sizing, centrifugation theory, aerosols, mineral processing, and environmental transport. Use measured viscosity at the actual temperature because liquid viscosity can change substantially with temperature. For experiments, allow enough distance for terminal motion and account for container-wall corrections. Treat the output as a clear first estimate, then select a more general drag correlation whenever the assumptions or Reynolds-number check are not satisfied.