Terminal Speed Calculator

Analyze falling objects across fluids with practical inputs. Compare drag, buoyancy, and stability in seconds. See terminal trends clearly with fast results and visuals.

Calculator Inputs

Plotly Graph

The graph compares drag force with the net downward force. Terminal speed appears where both become equal.

Example Data Table

Case Model Key Inputs Terminal Speed (m/s) Terminal Speed (km/h)
Baseball in air Quadratic m=0.35, A=0.018, Cd=0.47, ρ=1.225 25.726 92.6135
Skydiver spread posture Quadratic m=80, A=0.70, Cd=1.10, ρ=1.225 40.7688 146.7678
Small grain in water Stokes r=0.0015, ρp=2650, ρf=1000, μ=0.001 8.0933 29.1357

Formula Used

Quadratic Drag Model

Terminal speed:

vt = √[2(mg − ρfVg) / (ρfCdA)]

Use this when drag grows with velocity squared. It suits larger objects and faster motion through air.

Stokes Flow Model

Terminal speed:

vt = 2r²g(ρp − ρf) / 9μ

Use this for small particles in laminar flow, where viscous drag changes linearly with velocity.

Symbol guide: m = mass, A = projected area, Cd = drag coefficient, ρ = density, V = object volume, r = particle radius, μ = dynamic viscosity.

Physics meaning: terminal speed occurs when downward effective weight equals upward drag force, so acceleration becomes zero.

How to Use This Calculator

  1. Choose the drag model that best matches your case.
  2. Enter dimensions, densities, viscosity, and gravity values.
  3. Use SI units for consistent and reliable output.
  4. Click the calculate button to generate the result.
  5. Review the summary table, speed conversions, and flow note.
  6. Use the Plotly graph to inspect the force balance.
  7. Download the result as CSV or PDF when needed.

Frequently Asked Questions

1. What is terminal speed?

Terminal speed is the constant speed reached during a fall when drag and buoyancy fully balance the object’s effective weight. Acceleration then becomes zero, so the speed stops increasing.

2. Why are there two different models?

Different flow regimes need different drag laws. Larger or faster objects often follow quadratic drag. Very small particles moving slowly through viscous fluids often follow Stokes flow.

3. When should I use the quadratic model?

Use the quadratic model for balls, people, droplets, and other objects moving fast enough that inertial drag dominates. It is common for air resistance problems and many engineering estimates.

4. When should I use the Stokes model?

Use the Stokes model for small particles in slow, smooth, laminar flow. It is especially useful in liquids, sedimentation studies, and particle settling estimates with low Reynolds numbers.

5. Why does fluid density matter?

Fluid density affects both drag and buoyancy. A denser fluid pushes upward more strongly and also increases resistance. That usually lowers terminal speed compared with the same object falling in a lighter fluid.

6. What does the drag coefficient represent?

The drag coefficient summarizes how shape, orientation, and surface behavior influence resistance. Streamlined objects have lower values, while bluff shapes usually have higher values.

7. Can this calculator be used for liquids and gases?

Yes. Enter the correct fluid density and viscosity for air, water, oil, or another fluid. Then choose the model that best matches the expected flow regime.

8. Why is my result invalid or missing?

Invalid results usually come from negative inputs, zero areas, zero viscosity, or a density combination that makes the object effectively float instead of settle downward.

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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.