Terminal Velocity Examples Calculator

Calculator Inputs

Example Data Table

Formula Used

Quadratic Drag Formula

Terminal velocity occurs when net downward force equals drag force.

v = √((2 × (m × g − ρf × V × g)) ÷ (ρf × Cd × A))

Here, m is mass. g is gravity. ρf is fluid density. V is object volume. Cd is drag coefficient. A is projected area.

Stokes Flow Formula

For very small spherical particles in viscous flow, use this relation.

v = (2 × r² × g × (ρp − ρf)) ÷ (9 × μ)

Here, r is particle radius. ρp is particle density. μ is dynamic viscosity. This model works best when Reynolds number stays below one.

Supporting Outputs

Re = ρf × v × L ÷ μ. The Reynolds number helps judge model choice. Dynamic pressure is q = 0.5 × ρf × v².

How to Use This Calculator

1. Choose the drag model or select the automatic option.
2. Enter mass, diameter, area, fluid density, and viscosity.
3. Leave area or volume as zero for estimated sphere values.
4. Enter drag coefficient for the quadratic drag method.
5. Choose an output unit and press the calculate button.
6. Review the Reynolds number and model note.
7. Download the result as a CSV or PDF file.

Understanding Terminal Velocity Examples

Why Terminal Velocity Matters

Terminal velocity is the steady speed reached by a falling object. At that point, downward effective weight equals upward resistance. The object stops accelerating, even while it keeps moving. This value matters in skydiving, rainfall, aerosols, sedimentation, ballistics testing, and laboratory demonstrations.

What This Calculator Evaluates

This calculator supports two useful examples. The quadratic drag method is best for larger objects in air or water. It uses mass, projected area, fluid density, drag coefficient, and buoyancy. It is often used for spheres, people, packages, and engineering bodies. The Stokes method is best for tiny spheres in viscous fluids. It uses particle radius, density difference, gravity, and dynamic viscosity. It is valid when flow is creeping and Reynolds number is very low.

Good Input Practice

Inputs should describe real geometry. Use projected frontal area for quadratic drag. A sphere can use pi times diameter squared divided by four. Use volume when buoyancy is important. If volume is blank, the tool can estimate it from diameter or density. Use the correct fluid density. Air, water, glycerin, and oil produce very different answers. Viscosity is also important for small particles and droplets.

Reading the Result

The result gives terminal speed in your selected unit. It also shows speed in meters per second, force balance, Reynolds number, dynamic pressure, and estimated time to reach ninety five percent of terminal speed. The time estimate is an approximation. It assumes the object starts from rest and the drag coefficient stays constant. Real objects may tumble, rotate, deform, or change area during descent.

Comparing Common Examples

Examples help check the inputs. A skydiver has a large area and high drag coefficient. A small steel ball has a small area and high density. A raindrop sits between these cases. A fine droplet in oil may require the Stokes model. The Reynolds number note helps judge the selected model. Low Reynolds number supports Stokes flow. Higher values usually require quadratic drag.

Practical Use

Use this calculator for education, estimates, and comparisons. For safety design, use measured coefficients and validated simulations. Wind, shape changes, turbulence, wall effects, and compressibility can change the final speed. Always match the model to the object and fluid before trusting the number. For reports, export the result and keep assumptions beside each example for review and later classroom comparison work.