What this calculator does
Stokes' Law Terminal Velocity works out falling speed of a small sphere through a viscous fluid once drag balances its weight. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulav = g·d²·(ρp − ρf) / (18·η) (valid for low Reynolds number, laminar flow)
The inputs explained
| Field | What to enter |
|---|---|
| Particle diameter (m) | A number, measured in m. Starts at 0.0001. |
| Particle density (kg/m³) | A number, measured in kg/m³. Starts at 2650. |
| Fluid density (water ≈ 1000, air ≈ 1.225) (kg/m³) | A number, measured in kg/m³. Starts at 1000. |
| Fluid dynamic viscosity (water ≈ 0.001) (Pa·s) | A number, measured in Pa·s. Starts at 0.001. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with particle diameter
Every other input is held at the calculator’s starting values while particle diameter varies. Select any row to load that scenario into the calculator.
How the answer changes with particle diameter
| Particle diameter (m) | Terminal velocity | Terminal velocity | Reynolds number at this speed |
|---|---|---|---|
| 0 | 0.0000e+0 m/s | 0.000 mm/s | 0 (Stokes flow: valid) |
| 0 | 0.0000e+0 m/s | 0.000 mm/s | 0 (Stokes flow: valid) |
| 0 | 0.0000e+0 m/s | 0.000 mm/s | 0 (Stokes flow: valid) |
| 0 | 0.0000e+0 m/s | 0.000 mm/s | 0 (Stokes flow: valid) |
| 0 | 0.0000e+0 m/s | 0.000 mm/s | 0 (Stokes flow: valid) |
| 0 | 0.0000e+0 m/s | 0.000 mm/s | 0 (Stokes flow: valid) |