Calculating Terminal Velocity in Physics

Analyze falling objects with flexible drag based inputs. Switch models and compare realistic physical assumptions. Download tables, save reports, and visualize velocity behavior instantly.

Calculator

Best for bluff bodies or faster motion where drag scales strongly with speed.
Best for small spheres in slow viscous flow.

Example data table

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

Formula used

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)].

How to use this calculator

  1. Select the drag model that matches your problem.
  2. Enter gravity, fluid density, and graph settings.
  3. For quadratic drag, enter mass, area, drag coefficient, and optional volume.
  4. For Stokes law, enter radius, object density, and viscosity.
  5. Press the calculate button.
  6. Read the result block above the form.
  7. Review the graph, table, and assumption note before using the answer.
  8. Export the summary using the CSV or PDF buttons.

What this calculator helps you study

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.

FAQs

1. What is terminal velocity?

Terminal velocity is the constant speed reached when the resistive force balances the effective downward force, so acceleration becomes zero.

2. Why are there two models?

Different flows behave differently. Faster or larger cases often use quadratic drag. Small slow spheres in viscous flow often use Stokes law.

3. When should I use the quadratic option?

Use it for objects such as people, balls, or equipment moving through air where shape and frontal area matter strongly.

4. When should I use the Stokes option?

Use it for small spherical particles moving slowly in a viscous fluid, especially when linear drag is a reasonable approximation.

5. Does buoyancy matter here?

Yes. The calculator subtracts displaced fluid weight where the model supports it, which reduces the effective downward force and terminal speed.

6. Why does projected area change terminal velocity?

A larger frontal area increases drag for the same speed. Stronger drag means the balance point is reached at a lower velocity.

7. What does the Reynolds number estimate tell me?

It gives a quick sense of flow regime. That helps you judge whether the selected drag model is likely reasonable.

8. Can I use this calculator for liquids?

Yes. Enter the liquid density and viscosity carefully. The same balance ideas apply, but the proper model choice becomes even more important.

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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.