Terminal Velocity Calculator

Mass (m):

Gravitational Acceleration (g):

Cross-Sectional Area (A):

Fluid Density (ρ):

Drag Coefficient (C_d):

Terminal Velocity (m/s): Terminal Velocity (km/h): Terminal Velocity (mph): Terminal Velocity (ft/s):

1. What is Terminal Velocity?

Definition: Terminal velocity is the constant maximum speed an object reaches when falling through a fluid, such as air or water, where the downward gravitational force is balanced by the upward drag force. At this point, the object no longer accelerates and moves at a steady speed.

Purpose: This concept is widely used to analyze the motion of falling objects, including skydivers, raindrops, or parachutes, in physics, engineering, and aerodynamics.

2. How Does the Calculator Work?

The calculator applies the terminal velocity formula:

\[ v_t = \sqrt{\frac{2 \cdot m \cdot g}{\rho \cdot A \cdot C_d}} \]

Where:

\( v_t \): Terminal velocity (m/s);
\( m \): Mass of the object (kg);
\( g \): Gravitational acceleration (m/s²);
\( \rho \): Fluid density (kg/m³);
\( A \): Cross-sectional area of the object (m²);
\( C_d \): Drag coefficient (unitless).

Unit Conversions:

Mass: 1 g = 0.001 kg, 1 lb = 0.453592 kg
Gravity: 1 ft/s² = 0.3048 m/s²
Area: 1 cm² = 0.0001 m², 1 ft² = 0.092903 m²
Density: 1 g/cm³ = 1000 kg/m³, 1 lb/ft³ = 16.0185 kg/m³
Velocity: 1 m/s = 3.6 km/h = 2.23694 mph = 3.28084 ft/s

Explanation: Users input values in their chosen units, which are converted to SI units (kg, m/s², m², kg/m³). The calculator then computes terminal velocity and displays it in m/s, km/h, mph, and ft/s, ensuring accuracy and versatility.

3. Importance of Terminal Velocity

Significance: Terminal velocity is critical for:

Predicting the maximum falling speed of objects, such as skydivers (~55 m/s belly-to-earth) or raindrops (~9 m/s).
Understanding fluid dynamics and aerodynamic behavior in various media, like air or water.
Designing safety equipment, such as parachutes, and analyzing falling objects in engineering applications.

4. Using the Calculator

Guidelines: Input the object’s mass, gravitational acceleration (default 9.81 m/s²), cross-sectional area, fluid density (default 1.225 kg/m³ for air), and select a shape or custom drag coefficient. Ensure all values are positive. Results are displayed with 3 decimal places in m/s, km/h, mph, and ft/s.

5. Frequently Asked Questions (FAQ)

Q: What happens if I enter negative values?
A: The calculator sets terminal velocity to 0 for invalid (negative or zero) inputs, as physical values must be positive.

Q: Why does terminal velocity vary for different shapes?
A: The drag coefficient (C_d) depends on shape, orientation, and surface texture, affecting how air resistance opposes gravity.

Q: Can this calculator be used for water instead of air?
A: Yes, adjust the fluid density (e.g., ~1000 kg/m³ for water) to calculate terminal velocity in different fluids.

Q: What is a typical terminal velocity for a skydiver?
A: A skydiver in a belly-to-earth position typically reaches ~55 m/s (about 200 km/h or 124 mph) in air.

Q: How accurate is the default fluid density?
A: The default 1.225 kg/m³ is for air at sea level (15°C, 1 atm), but it varies with altitude, temperature, and pressure—adjust as needed.