Terminal Velocity Output
The result appears here above the form after submission.
Calculator Inputs
Large screens use three columns. Smaller screens use two. Mobile uses one.
Velocity and Drag Graph
The graph compares drag force with the balancing force and marks the terminal point.
Example Data Table
| Case | Model | Mass / Radius | Area / Density | Fluid | Useful Note |
|---|---|---|---|---|---|
| Baseball in air | Quadratic drag | 0.145 kg | 0.0042 m², Cd 0.47 | Air, 1.225 kg/m³ | Good everyday example for outdoor motion. |
| Glass bead in water | Stokes law | 0.0005 m radius | 2500 kg/m³ object density | Water, 998.2 kg/m³ | Useful for slow small-particle settling studies. |
Formula Used
Quadratic Drag
Balance: m g = 0.5 rho Cd A vt2
Terminal velocity: vt = sqrt((2 m g) / (rho Cd A))
Stokes Law
Balance: 6 pi mu r vt = (4/3) pi r3 (rhop - rhof) g
Terminal velocity: vt = (2 r2 (rhop - rhof) g) / (9 mu)
Use the Stokes form only for very small spheres in slow laminar flow.
How to Use This Calculator
- Pick a model that matches the object and flow regime.
- Choose a fluid preset or keep custom fluid values.
- Enter mass, area, and drag coefficient for quadratic drag.
- Enter radius, densities, and viscosity for Stokes law.
- Set gravity if you are using a nonstandard environment.
- Press calculate to show the result above the form.
- Review the graph, notes, and unit conversions.
- Download CSV or PDF when you need a report.
About Terminal Velocity
Understanding Terminal Velocity
Terminal velocity is the steady speed of a falling object. It appears when downward force equals upward drag and buoyancy effects. At that moment, acceleration becomes zero. The object keeps moving, but it no longer speeds up. This idea matters in physics, engineering, and safety analysis.
Why the Value Changes
Terminal velocity depends on mass, shape, area, and fluid properties. A heavier object often falls faster when size stays similar. A larger area increases drag and lowers the final speed. Dense fluids also slow motion more strongly. Air and water give very different results. Drag coefficient matters because smooth and rough shapes resist flow differently.
Two Common Models
The quadratic drag model suits many everyday falling cases in air. It uses mass, gravity, drag coefficient, frontal area, and fluid density. This model is common for balls, equipment, and many outdoor objects. The Stokes model is different. It works for very small spheres moving slowly in viscous fluids. It uses radius, densities, viscosity, and gravity. That model is useful for droplets, beads, and fine particles.
How to Read the Output
The calculator reports terminal velocity in several units. It also shows drag force at equilibrium. For the quadratic model, weight balances drag at the final speed. For the Stokes model, the result may be negative. That means the object tends to rise instead of fall. Reynolds number is also useful for checking whether Stokes assumptions remain reasonable.
Practical Use
Use this calculator for study, lab planning, and quick design checks. It helps compare shapes, fluids, and object sizes. You can test custom densities and viscosities. You can also export results for reports or coursework. Always remember that real motion can include turbulence, spin, and changing orientation. Those effects can shift the actual value. Treat the result as a strong estimate, then confirm with measured data when precision matters most.
Good inputs produce good estimates. Measure area carefully and choose a realistic drag coefficient. For unusual shapes, test several coefficient values and compare trends. In water or oil, viscosity becomes more important. Sensitivity checks can reveal which variable controls the result most strongly for your case during early planning.
Frequently Asked Questions
1. What is terminal velocity?
Terminal velocity is the constant speed reached when drag balances the driving force. At that point, acceleration becomes zero, so the object keeps moving without further speeding up.
2. Does a heavier object always have a higher terminal velocity?
Not always. Mass can raise terminal velocity, but area and drag coefficient matter too. A light, compact object may fall faster than a larger, flatter heavy object.
3. Which model should I choose?
Use the quadratic model for many everyday objects moving through air. Use the Stokes model for very small spheres in slow, viscous flow.
4. What is projected area?
Projected area is the front-facing area normal to motion. For a sphere, use the circle area. For flat objects, use the area facing the flow.
5. Is this calculator exact?
It is an estimate. Real motion can change with spin, turbulence, posture, deformation, and altitude. Measured tests are still best for critical design work.
6. Why can Stokes law return a negative value?
A negative Stokes result means buoyancy exceeds the downward effective weight. The object tends to rise through the fluid instead of sinking.
7. Can I use fluids other than air?
Yes. Density and viscosity strongly affect drag. Air, water, oil, and custom fluids can produce very different terminal velocities for the same object.
8. What are the main limits of these formulas?
The quadratic formula assumes drag dominates and values stay reasonably steady. The Stokes formula assumes slow, laminar motion around a small sphere.