Free Fall with Air Resistance Calculator

Calculate fall time, terminal velocity, and drag forces including air resistance effects

Traveling Object Parameters

Mass of the falling object

Height from which the object falls

m/s²

Earth: 9.807 m/s² • Moon: 1.62 m/s² • Mars: 3.71 m/s²

kg/m

Skydiver: 0.24 kg/m • Sphere: varies • Calculate below for custom objects

Calculate Air Resistance Coefficient (Optional)

Time and Velocity Results

40.04
seconds
Time of Fall
55.36
m/s
Maximum Velocity
55.36
m/s
Terminal Velocity

Terminal Velocity Analysis

Percentage of Terminal Velocity Reached: 100.0%
Final Velocity at Impact: 55.36 m/s
Air Resistance Coefficient: 0.240000 kg/m
Terminal Velocity Formula: vt = √(mg/k)

Terminal velocity reached! The object has reached approximately 100.0% of its terminal velocity.

Drag Force Calculator

Velocity at which to calculate drag force

0.00
N
Drag Force

Formula: F = k × v² = 0.240000 × 0.00² = 0.00 N

Example Calculations

Skydiver Example

Mass: 75 kg

Altitude: 2000 m

Air resistance (k): 0.24 kg/m

Terminal velocity: √(75×9.807/0.24) = 55.4 m/s

Result: Reaches terminal velocity before impact

Feather vs. Ball

Feather: High air resistance, low terminal velocity

Steel ball: Low air resistance, high terminal velocity

In vacuum: Both fall at same rate

In air: Ball falls much faster than feather

Sphere in Air

Sphere radius: 0.1 m

Area: π × 0.1² = 0.0314 m²

Drag coefficient: 0.47

k: (1.225 × 0.0314 × 0.47) / 2 = 0.009 kg/m

High Altitude Jump

Altitude: 39,000 m (stratosphere)

Lower air density: Affects air resistance

Higher terminal velocity: Due to thinner air

Felix Baumgartner: Exceeded speed of sound

Air Resistance Physics

Drag Force

F = k × v² where k is air resistance coefficient

Terminal Velocity

When drag force equals gravitational force: vt = √(mg/k)

Air Resistance Coefficient

k = ρ × A × Cd / 2 (density × area × drag coefficient)

Typical Drag Coefficients

Sphere0.47
Cube1.05
Human (standing)1.0-1.3
Cylinder0.82
Streamlined body0.04
Parachute1.3-1.5

Medium Densities

Air (15°C)1.225 kg/m³
Air (0°C)1.293 kg/m³
Water (20°C)998 kg/m³
Glycerin1260 kg/m³
Oil900 kg/m³

Physics Tips

Air resistance increases with the square of velocity

Terminal velocity depends on mass, area, and drag coefficient

Streamlined objects have lower drag coefficients

Higher altitude means lower air density and higher terminal velocity

Understanding Free Fall with Air Resistance

What is Air Resistance?

Air resistance, also called drag force, is a force that opposes the motion of objects through air. Unlike ideal free fall, real-world objects experience this force that increases with velocity, ultimately limiting their maximum speed.

Key Physics Principles

  • Drag force equation: F = k × v² (quadratic with velocity)
  • Terminal velocity: Maximum speed when F_drag = mg
  • Shape matters: Streamlined objects fall faster
  • Medium density: Affects drag coefficient calculation

Real-world Applications

Skydiving: Understanding terminal velocity for safety

Parachutes: Dramatically increase drag to reduce terminal velocity

Aerospace: Designing for minimal drag in aircraft and spacecraft

Famous Examples

  • Galileo's Tower of Pisa experiment
  • Apollo 15 hammer and feather drop on Moon
  • Felix Baumgartner's supersonic freefall
  • Raindrop terminal velocity research

Mathematical Relationships

F = k × v²

Drag force equation

vt = √(mg/k)

Terminal velocity

k = ρACd/2

Air resistance coefficient