Stokes Settling Velocity Calculator
Introduction to Stokes Settling Velocity
Stokes settling velocity is the terminal speed a small sphere reaches as gravity pulls it through a viscous fluid and drag builds until the two balance. This calculator turns that balance into a quick estimate for particles such as mineral grains, droplets, cells, or pigment spheres, making it useful anywhere you need to know whether material will stay suspended or separate on its own. In treatment tanks, lab cylinders, product formulations, and environmental samples, the question is often not whether a particle can settle, but how long that settling will take.
The answer here is a first-pass Stokes-law estimate for conditions where the flow around the particle is gentle and orderly. That makes it a practical screening tool for comparing sizes, fluids, and density contrasts before you move to a bench test or a more detailed drag model. The calculator also reports Reynolds number because Stokes’ law only behaves well when the particle-scale Reynolds number stays very low.
How to Use This Calculator for Particle Settling
Enter the particle radius in meters, the particle and fluid densities in kilograms per cubic meter, the fluid viscosity in pascal-seconds, and local gravity in meters per second squared. The calculator uses SI units throughout, so micron-sized particles must be converted before you type them in; 10 micrometers, for example, is 1e-5 m. If your values come from a data sheet, density is usually straightforward, while viscosity often depends on temperature and composition.
Once you compute the result, read the settling velocity as the terminal speed after the particle has stopped accelerating. A positive value means the particle sinks; a negative value means buoyancy wins and the particle rises instead. The Reynolds number shown alongside the velocity tells you whether the low-Reynolds assumption is still believable or whether the motion is starting to leave the Stokes regime.
Stokes’ Law Formula for Settling Velocity
For a sphere moving slowly through a Newtonian fluid, the viscous drag is proportional to speed, and balancing that drag against the particle’s effective weight gives the standard Stokes expression:
In the equation, is particle density, is fluid density, is gravitational acceleration, is particle radius, and is dynamic viscosity.
Several practical lessons fall directly out of that formula. The speed depends on the density difference between particle and fluid, not on particle density alone, so a heavy particle can still settle slowly if the surrounding fluid is nearly as dense. The radius appears squared, which means size has a very strong influence: doubling radius makes the settling velocity four times larger if everything else stays fixed. Viscosity sits in the denominator, so thicker fluids slow motion in direct proportion. If viscosity rises by a factor of ten, settling speed falls by a factor of ten. Those relationships explain why fine clay can remain suspended in water, why larger sand grains drop out much faster, and why particles crawl through syrups, oils, or polymer solutions.
Worked Example: a 10 µm Mineral Particle in Water
Consider a mineral particle with radius 10 µm, density 2500 kg/m³, settling through water with density 1000 kg/m³ and viscosity 0.001 Pa·s at ordinary Earth gravity. Converting the radius gives 1e-5 m, and the density contrast is 1500 kg/m³. Plugging those values into Stokes’ law gives a settling velocity of about 3.27 × 10-4 m/s, or 0.327 mm/s. That is slow on human scales, but in a quiescent column it is enough to produce visible settling over a practical lab time.
If you keep the same particle but double the radius to 20 µm, the r² term makes the predicted speed four times larger, not just twice as large. If instead you keep the 10 µm radius and raise the viscosity from 0.001 to 0.01 Pa·s, the settling speed drops by a factor of ten. Those two comparisons are often more helpful than a single output because they show whether size, viscosity, or density contrast is the main lever in your system.
Interpreting the Result for Settling Time
The velocity output is the terminal speed, not the travel distance, so use it together with the fluid depth when you want a settling time estimate. A compact way to do that is:
For example, if a particle settles at 2 × 10-5 m/s through a 5 cm fluid layer, the travel time is about 2500 seconds, or roughly 42 minutes. That kind of estimate is often enough to judge whether a clarifier, jar test, or storage tank will separate particles on the timescale you need.
Also watch the sign. Positive values mean downward settling; negative values mean the particle is lighter than the fluid and will rise. If the velocity is very close to zero, buoyancy and weight nearly cancel, so tiny currents, agitation, or Brownian motion may influence what you see more than gravity alone.
Assumptions, Validity, and Reynolds Number for Stokes Settling
Stokes settling velocity is elegant because it compresses a fluid-mechanics problem into one formula, but the calculator is only trustworthy when the particle and fluid match the assumptions behind that formula. The particle should be spherical or close to spherical, the suspension should be dilute enough that neighboring particles do not strongly interfere, the fluid should behave as a Newtonian liquid, and the flow around the particle should remain laminar. Wall effects should also be small, so the particle ideally settles in a container much wider than its own diameter. If any of those assumptions fail, the result becomes a rough estimate rather than a dependable prediction.
The usual first check is the Reynolds number:
When is below about 0.1, the Stokes regime is generally a good approximation. As Reynolds number grows, inertial effects become more important, the drag law changes, and the true settling velocity will deviate from the calculator’s value. This page therefore reports Reynolds number alongside the main answer so you can judge whether the low-Reynolds assumption is likely to hold. A very small Reynolds number is reassuring; a value near or above 0.1 is a signal to verify the problem with a more general drag correlation.
Why This Matters in Practice for Sedimentation
In practice, Stokes settling velocity is a shortcut for deciding whether a suspension will separate quickly enough to matter. In environmental engineering, the same calculation helps size sedimentation basins, grit chambers, and clarifiers so particles have enough residence time to drop out before the cleaned water leaves the tank. In mineral processing, it helps estimate whether a slurry will classify by size under gravity. In pharmaceutical suspensions, the goal is often the opposite: a product should remain visually uniform on the shelf, which means slow settling is desirable. A viscosity modifier, a smaller particle size, or a lower density contrast can all help achieve that goal.
Food and consumer products provide familiar examples too. Cocoa particles settle in chocolate milk, spices separate in sauces, pigments drop in paints, and fragrance capsules can rise or sink depending on formulation density. Stokes’ law does not capture every real-world complication, but it gives immediate physical intuition. If a product suddenly separates after reformulation, the cause is often not mysterious at all: the particles may have grown larger, the fluid may have thinned, or the density contrast may have increased.
Environmental and Biological Systems
Natural and biological suspensions rarely look as tidy as a glass cylinder, but the same settling physics still helps you reason about them. Fine sediment in lakes, quiet reaches of rivers, atmospheric particles settling from air, and planktonic material in water columns all respond to the same balance between effective weight and drag. In biology and biotechnology, cells, spores, beads, and organelles may settle under similar principles during handling, washing, or low-speed centrifugation. Researchers often begin with a Stokes-style estimate before adding corrections for shape, porosity, aggregation, or flow disturbances.
Beyond Perfect Spheres
Most real particles are not perfect spheres, and that shape difference usually slows them down. Flakes, rods, fibers, and irregular fragments create more drag than a sphere of the same volume, so the calculator’s result should be treated as a benchmark rather than a promise when the particle is not round. Engineers may use a shape factor, an equivalent spherical diameter, or experimentally measured drag data when accuracy matters. If you are applying this calculator to non-spherical material, think of it as the settling speed an ideal sphere would have under the same conditions.
Hindered Settling and Concentration Effects
This calculator treats one particle at a time, so it cannot account for crowded suspensions. In concentrated slurries, neighboring particles disturb the fluid and slow one another down, a phenomenon called hindered settling. This effect becomes important in sludge blankets, thickeners, and dense process streams where the fluid displaced by one particle must weave around many others. Under those conditions, the single-particle result from this calculator is usually an upper bound rather than the true bulk settling speed.
Choosing Reliable Inputs for a Settling Estimate
Getting meaningful settling estimates starts with matching the inputs to the actual particle and fluid you are studying. Particle radius should represent the settling particle itself, not the radius of an agglomerate unless aggregation is truly present in the fluid. Density should match the specific material and, when possible, the actual temperature of the experiment or process. Viscosity deserves special care because it can shift strongly with temperature and composition. A fluid that behaves like water at one condition may act much more like a syrup after cooling or after dissolved solids are added. If your answer seems surprising, check unit conversion first, then confirm whether the viscosity value truly belongs to the fluid state you are modeling.
A practical habit is to vary one input at a time and see how sensitive the result is. If a small uncertainty in radius changes the settling speed a great deal, then measuring particle size more accurately may matter more than refining density to a third decimal place. This kind of sensitivity thinking is one of the most useful outcomes of using a calculator like this. It helps you decide where to spend experimental effort and where a rough estimate is already good enough for planning.
Laboratory Tips for Stokes Settling Experiments
When you use Stokes settling velocity to plan a bench experiment, the setup details matter as much as the numbers you enter. Make sure the fluid is as quiescent as possible before timing the motion, record temperature so you can choose an appropriate viscosity, use a vessel wide enough to reduce wall effects, and measure particle size carefully because the radius-squared dependence makes size errors especially costly. A 10% uncertainty in radius becomes roughly a 20% uncertainty in settling velocity. That sensitivity is one reason particle-sizing methods are so important in suspension science.
When the Stokes Estimate Stops Being Enough
The calculator is still useful even when the full system is messier than ideal Stokes flow, because it tells you which direction each change should push the settling speed. If Reynolds number is not very small, if the particle is porous or deformable, if the fluid is non-Newtonian, or if many particles are settling together, then the system has moved beyond classical Stokes behavior. Even then, the result remains a valuable baseline. It shows the effect of changing particle size, density contrast, viscosity, or gravity, and it often tells you whether you are in the right ballpark before moving to a more advanced model or a laboratory test.
That is why Stokes’ law appears so often in teaching, screening calculations, and early-stage design. It condenses a lot of physical reasoning into one short equation without hiding what matters. Bigger particles settle faster. Stronger buoyancy contrast pushes motion harder. More viscous fluids resist motion more strongly. Stronger gravity speeds the process. Those simple statements are exactly what the calculator turns into numbers.
Example Velocities for Stokes Settling
The table below gives order-of-magnitude settling velocities for a particle density of 2500 kg/m³ and a fluid density of 1000 kg/m³ unless noted. The point is not the exact number but the pattern: increasing radius strongly speeds up settling, while increasing viscosity slows it dramatically.
| Particle Radius (µm) | Fluid | Velocity (mm/s) |
|---|---|---|
| 1 | Water | 0.0033 |
| 5 | Water | 0.0818 |
| 10 | Oil (η = 0.05 Pa·s) | 0.0065 |
Conclusion: using Stokes settling velocity as a screening tool
This Stokes Settling Velocity Calculator is best treated as a quick screening tool for small spherical particles in viscous fluids. It shows how particle size, density contrast, viscosity, and gravity work together, and it reports Reynolds number so you can judge whether the low-Reynolds assumption is plausible. If the inputs describe a small, nearly spherical particle in a dilute Newtonian fluid and the Reynolds number stays small, the result is a good estimate for comparing formulations or estimating separation time. If not, it still gives a sound baseline for deciding when to move to a more detailed model or an experiment.
Use SI units for every field: radius in meters, densities in kg/m³, viscosity in Pa·s, and gravity in m/s². Example conversion: 10 µm = 1e-5 m.
Mini-Game: Clarifier Control for Settling Velocity
This optional mini-game turns Stokes settling into a timing challenge. Route each feed particle into the lane whose viscosity best matches the release timing, then try to open the collector window when the particle arrives. It mirrors the calculator's logic without changing the underlying equation.
Formula hint: settling speed rises with density contrast and the square of particle radius, and falls as viscosity increases. During special phases, temperature or gravity changes may shift the timing.