Analyze falling objects with flexible drag based inputs. Switch models and compare realistic physical assumptions. Download tables, save reports, and visualize velocity behavior instantly.
| Case | Model | Key inputs | Approximate output |
|---|---|---|---|
| Skydiver | Quadratic drag | m = 80 kg, A = 0.7 m², Cd = 1.0, ρf = 1.225 kg/m³, V = 0.075 m³ | vt ≈ 42.759 m/s |
| Baseball | Quadratic drag | m = 0.145 kg, A = 0.0042 m², Cd = 0.47, ρf = 1.225 kg/m³, V = 0.000069 m³ | vt ≈ 34.290 m/s |
| Small particle | Stokes law | r = 0.00002 m, ρp = 2500 kg/m³, ρf = 1.2 kg/m³, μ = 0.000018 Pa·s | vt ≈ 0.121 m/s |
Quadratic drag model
At terminal velocity, effective weight equals drag.
m g − ρf V g = (1/2) ρf Cd A vt²
vt = √[ 2 (m − ρf V) g / (ρf Cd A) ]
Stokes law model for a sphere
At terminal velocity, excess weight equals viscous drag.
(ρp − ρf) g (4/3) π r³ = 6 π μ r vt
vt = 2 r² g (ρp − ρf) / (9 μ)
Velocity growth for the graph
Quadratic drag uses vt tanh(g_eff t / vt).
Stokes law uses vt [1 − exp(−t / τ)].
This calculator estimates terminal velocity for falling objects in fluids. It supports a broad drag balance model and a viscous sphere model. That makes it useful for classroom examples, lab planning, and quick comparisons between body shapes, densities, and fluid conditions.
The quadratic option suits many macroscopic objects in air, such as sports balls or skydivers. The Stokes option suits small spherical particles in slower viscous motion. You can compare how area, mass, density, viscosity, and drag coefficient alter the limiting speed.
The result table also reports a characteristic time and an estimated Reynolds number when the required inputs are available. These extra values help you judge whether the chosen model is physically sensible for your case.
Terminal velocity is the constant speed reached when the resistive force balances the effective downward force, so acceleration becomes zero.
Different flows behave differently. Faster or larger cases often use quadratic drag. Small slow spheres in viscous flow often use Stokes law.
Use it for objects such as people, balls, or equipment moving through air where shape and frontal area matter strongly.
Use it for small spherical particles moving slowly in a viscous fluid, especially when linear drag is a reasonable approximation.
Yes. The calculator subtracts displaced fluid weight where the model supports it, which reduces the effective downward force and terminal speed.
A larger frontal area increases drag for the same speed. Stronger drag means the balance point is reached at a lower velocity.
It gives a quick sense of flow regime. That helps you judge whether the selected drag model is likely reasonable.
Yes. Enter the liquid density and viscosity carefully. The same balance ideas apply, but the proper model choice becomes even more important.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.