In 1851, George Gabriel Stokes worked out the drag force on a small sphere creeping through a viscous fluid — a result that still underpins sediment analysis, viscometry, and particle-size measurement today. This calculator applies F = 6πµrv to find drag directly, or rearranges the force balance between gravity, buoyancy, and drag to find how fast a particle settles (or rises) through a fluid.
How the Stokes' Law Calculator works
Stokes' drag force, F = 6πµrv, comes from solving the fluid-flow equations for a sphere moving slowly enough that inertia is negligible compared to viscous friction — the so-called creeping-flow regime. The settling velocity formula extends this by setting drag equal to the net downward force of gravity minus buoyancy (which depends on the density difference between the particle and the fluid), then solving for the velocity at which those forces balance. Because that balance can favor either direction, a particle less dense than the surrounding fluid will rise rather than settle — the calculator reports this explicitly rather than treating it as an error.
Inputs and what they mean
Radius (m) is the sphere's radius, not diameter — Stokes' law is derived specifically for spheres, so irregularly shaped particles need a shape-correction factor this calculator does not apply. Dynamic viscosity µ (Pa·s) is a property of the fluid; water is about 0.001 Pa·s while glycerin is roughly 1.49 Pa·s. Particle density and fluid density (kg/m³) only matter for the settling-velocity calculation — their difference, not their absolute values, drives the result. Velocity (m/s) on the Drag Force tab is the relative speed between the sphere and the fluid, however that motion arises.
Limits and edge cases
Stokes' law is only accurate in the low-Reynolds-number (creeping-flow) regime, roughly Re ≪ 1, where Re = ρf·v·(2r)/µ using the sphere's diameter. Above about Re = 1 the flow starts separating from the back of the sphere, and real-world drag exceeds the Stokes prediction — the Settling Velocity tab flags this with a Reynolds-number check. The formula also assumes an infinite, still, Newtonian fluid; it does not account for nearby container walls (the 'wall effect'), particle-particle interactions in concentrated suspensions, non-spherical shapes, or compressible or non-Newtonian fluids. For fast-falling or larger particles, use a full drag-coefficient correlation instead.