Terminal Velocity Calculator

Author: Henrick Yau
- May 14, 2025
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Calculators

Terminal velocity is the maximum velocity attainable by an object falling through a fluid. It occurs when the sum of the drag force and buoyancy equals the downward force of gravity, resulting in zero net acceleration.

This calculator helps you determine the terminal velocity of an object based on its properties and the fluid it's falling through.

? The area of the object perpendicular to the direction of motion. For a falling person in the spread position, it's approximately 0.7-1.0 m².
Cd
? Drag coefficient depends on object shape. Typical values: sphere (0.47), cube (1.05), human skydiver (0.7-1.2).

Fluid Properties

Advanced Options

About Terminal Velocity

Terminal velocity is the steady speed achieved by a falling object when the drag force and buoyancy equal the gravitational force. At this point, the net force becomes zero, and the object stops accelerating.

Key Factors Affecting Terminal Velocity:
  • Object Mass and Size: Heavier objects with smaller cross-sectional areas reach higher terminal velocities.
  • Object Shape: The drag coefficient varies based on shape. Streamlined objects experience less drag.
  • Fluid Density: Denser fluids (like water compared to air) create more drag, resulting in lower terminal velocities.
  • Gravity: Higher gravitational acceleration increases terminal velocity.
Common Examples:
  • Human Skydiver: Approximately 55 m/s (120 mph) in spread position; up to 90 m/s (200 mph) in head-down position.
  • Raindrop: 9 m/s (20 mph) for medium-sized drops.
  • Hailstone (2cm): About 20 m/s (45 mph).
  • Baseball: Around 40 m/s (90 mph).
Practical Applications:
  • Skydiving: Understanding terminal velocity helps skydivers control their fall rate and relative positioning.
  • Meteorology: Predicting rainfall rates and precipitation time.
  • Engineering: Designing parachutes, air resistance systems, and predicting falling object behavior.
  • Space Exploration: Understanding atmospheric entry dynamics of spacecraft and objects.

What determines an object's terminal velocity?

The Terminal Velocity Calculator helps determine the maximum speed an object can reach while falling through a fluid, such as air or water. Terminal velocity occurs when the force of gravity pulling the object downward is balanced by the resistance (drag force) of the fluid, causing no further acceleration.

This tool allows users to calculate terminal velocity for different objects, including:

  • Standard objects with mass and cross-sectional area.
  • Spherical objects, such as balls or raindrops.
  • The human body in different falling positions.

Terminal Velocity Formula

The calculator uses the following equation to determine terminal velocity:

For a general object:

\[ v_t = \sqrt{\frac{2mg}{\rho A C_d}} \]

Where:

  • \( v_t \) = Terminal velocity (m/s)
  • \( m \) = Mass of the object (kg)
  • \( g \) = Gravitational acceleration (9.81 m/s² on Earth)
  • \( \rho \) = Density of the fluid (kg/m³)
  • \( A \) = Cross-sectional area of the object (m²)
  • \( C_d \) = Drag coefficient (dimensionless, varies by shape)

For a spherical object:

\[ v_t = \sqrt{\frac{8rg(\rho_s - \rho_f)}{3C_d \rho_f}} \]

Where:

  • \( r \) = Radius of the sphere (m)
  • \( \rho_s \) = Density of the sphere (kg/m³)
  • \( \rho_f \) = Density of the fluid (kg/m³)

How to calculate terminal velocity for any object

The calculator is user-friendly and allows input customization for different objects and fluids. Follow these steps:

  1. Select a Calculation Method: Choose between Standard, Sphere, or Human Body.
  2. Enter Object Properties: Input mass, cross-sectional area, or diameter and density, depending on the chosen method.
  3. Choose a Fluid: Select air at different altitudes, water, or a custom fluid with specific density.
  4. Adjust Additional Parameters: Set gravitational acceleration and drag coefficient (if applicable).
  5. Click "Calculate": The results will display terminal velocity, fall time, and impact force.

Why is Terminal Velocity Important?

Understanding terminal velocity has real-world applications in various fields:

  • Skydiving: Helps skydivers control their fall rate by adjusting body position.
  • Engineering: Used in parachute design and aerodynamics testing.
  • Meteorology: Predicts the fall speed of raindrops and hailstones.
  • Space Exploration: Crucial for calculating atmospheric re-entry speeds.

Questions about terminal velocity calculations

What affects terminal velocity?

Terminal velocity depends on object mass, shape, fluid density, and gravitational force. A larger mass or smaller drag coefficient results in a higher terminal velocity.

Does terminal velocity change with altitude?

Yes, air density decreases with altitude, reducing drag force and increasing terminal velocity. For example, a skydiver falls faster at higher altitudes due to thinner air.

Why do heavier objects fall faster?

Although gravity accelerates all objects equally, heavier objects require more force to slow them down. As a result, they reach a higher terminal velocity compared to lighter objects.

How does body position affect a falling person?

A spread-eagle position creates more air resistance, lowering terminal velocity (about 55 m/s). A head-down position reduces drag, increasing terminal velocity (up to 90 m/s).

Why this tool helps in physics and engineering

The Terminal Velocity Calculator is a useful tool for understanding how objects fall through different fluids. By entering key parameters, users can estimate terminal velocity and related effects, making it valuable for physics studies, sports science, and engineering applications.

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