Calculator Inputs
Formula Used
Quadratic Drag Model
vt = √(2mg / ρCdA)
Here, m is mass, g is gravity, ρ is fluid density, Cd is drag coefficient, and A is projected area.
Stokes Sphere Model
vt = 2r²(ρs - ρ)g / 9μ
Here, r is sphere radius, ρs is object density, ρ is fluid density, and μ is dynamic viscosity.
Reynolds Number
Re = ρvL / μ
A low Reynolds number supports Stokes flow. A high value usually supports a drag based model.
How to Use This Calculator
- Select the model. Use quadratic drag for many large objects.
- Use Stokes flow for tiny spheres moving slowly in viscous fluids.
- Enter all values in SI units for reliable results.
- Press the calculate button.
- Read the terminal speed, Reynolds number, and regime note.
- Use the CSV or PDF button to save the result table.
Example Data Table
| Example | Mass | Fluid Density | Cd | Area | Best Model | Note |
|---|---|---|---|---|---|---|
| Skydiver, belly position | 80 kg | 1.225 kg/m³ | 1.0 | 0.7 m² | Quadratic | Large area creates strong drag. |
| Dense metal ball in air | 0.5 kg | 1.225 kg/m³ | 0.47 | 0.003 m² | Quadratic | Sphere drag coefficient is useful. |
| Small particle in glycerin | Density based | 1260 kg/m³ | Not needed | Radius based | Stokes | Viscosity dominates motion. |
| Parachute load | 90 kg | 1.225 kg/m³ | 1.5 | 25 m² | Quadratic | Large area lowers terminal speed. |
Terminal Velocity in Physics
Core Meaning
Terminal velocity describes a steady falling speed. It appears when downward weight is balanced by upward drag. At that point, acceleration becomes zero. The body still moves, but its speed no longer rises.
Model Choice
This calculator uses two common models. The quadratic drag model works well for many objects moving through air at moderate and high Reynolds numbers. It needs mass, gravity, fluid density, drag coefficient, and projected area. The result grows when mass or gravity rises. It falls when the fluid becomes denser, the shape creates more drag, or area becomes larger.
Stokes Flow
The Stokes model is different. It is intended for tiny spheres moving slowly through a viscous fluid. It uses sphere radius, object density, fluid density, gravity, and dynamic viscosity. It is most reliable when the Reynolds number is below one. Larger Reynolds values mean inertia becomes important, so the quadratic model may be more suitable.
Input Units
Inputs should use consistent SI units. Mass is entered in kilograms. Area is entered in square meters. Radius is entered in meters. Fluid density is entered in kilograms per cubic meter. Dynamic viscosity is entered in pascal seconds. These units keep the formulas stable and make comparison easier.
Advanced Checks
The advanced fields help you explore sensitivity. You can add an uncertainty percentage to create an upper and lower range. You can also enter a fall distance and a target speed fraction. The tool estimates speed after that distance using the quadratic drag curve. It also estimates the time needed to approach a percentage of terminal speed.
Practical Limits
Real objects are not perfect. Drag coefficient changes with shape, surface roughness, and speed. A falling person, a sphere, a raindrop, and a parachute all behave differently. Air density also changes with altitude and temperature. Water density changes with salinity and temperature. For engineering work, test data should be used when available.
Best Use
Use this tool for learning, checks, laboratory planning, and design estimates. Compare both models when the object is small or the fluid is thick. Review the Reynolds number note before trusting the result. A low Reynolds number supports Stokes flow. A high Reynolds number supports a drag based estimate today.
FAQs
What is terminal velocity?
Terminal velocity is the steady speed reached when drag balances weight. The object keeps falling, but its acceleration becomes zero.
Which model should I use?
Use quadratic drag for large or fast objects. Use Stokes flow for tiny spheres moving slowly through viscous fluids.
What units should I enter?
Use SI units. Enter mass in kilograms, area in square meters, radius in meters, density in kilograms per cubic meter, and viscosity in pascal seconds.
Why is drag coefficient important?
Drag coefficient represents shape resistance. A higher value creates more drag and lowers the terminal velocity.
Can terminal velocity be negative?
In the Stokes model, a negative value means buoyancy is stronger than object weight. The object may rise instead of sink.
What does Reynolds number show?
Reynolds number indicates flow behavior. Low values support Stokes flow. High values suggest inertia and quadratic drag are more important.
Does air density change the answer?
Yes. Denser air creates stronger drag, so terminal velocity decreases. Thin air usually allows a higher falling speed.
Is this suitable for engineering design?
It is useful for estimates and study. For final design, compare results with experiments, standards, or validated simulation data.