Terminal Velocity Calculator

Use Terminal Velocity (Maximum Falling Speed) calculator to calculate maximum falling speed of an object for given mass of the falling object,acceleration due to gravity,density of fluid ,projected area of the object and drag coefficient.

Terminal Velocity Calculator - Maximum Falling Speed of an Object
Mass of the Falling Object
Acceleration Due to Gravity
Density of Fluid
Projected Area of the Object
Drag Coefficient
Terminal Velocity: {{terminalVelocityResult() | number:4}}

Termninal Velocity Formula:

Vt = √ ((2 x m x g) / (ρ x A x Cd))

Where,

Vt = Terminal Velocity (Maximum Falling Speed)

m = Mass of the Falling Object

g = Acceleration due to Gravity

ρ = Density of Fluid

A = Projected Area of the Object

Cd = Drag Coefficient

Frequently Asked Questions

What is terminal velocity and why do falling objects reach it?

Terminal velocity is the constant maximum speed an object reaches when falling through a fluid (air or water). Initially, gravity accelerates the falling object, increasing speed. As speed increases, drag force grows with the square of velocity, opposing gravity. Terminal velocity is reached when drag force exactly balances gravitational force, producing zero net acceleration. At this point, velocity remains constant despite continued gravitational pull.

What factors affect terminal velocity of a falling object?

Terminal velocity increases with object mass (heavier objects fall faster) and decreases with projected area and drag coefficient (more resistance lowers speed). For example, a parachutist falling at ~60 m/s without parachute reaches ~5 m/s with parachute open because the parachute dramatically increases drag area and coefficient. Understanding these relationships is essential for designing safe descent systems and predicting fall speeds.

How do different object shapes affect terminal velocity through drag coefficient?

Drag coefficient (Cd) depends strongly on shape. Streamlined shapes (teardrops, arrows) have Cd ≈ 0.04, minimizing drag. Bluff shapes (spheres, cylinders, parachutes) have Cd ≈ 0.47 to 1.5. Objects falling point-first achieve higher terminal velocity than broadside due to lower Cd. This is why skydivers can control fall rate by changing body position and why streamlined cars are more fuel-efficient.

When are terminal velocity assumptions valid in real scenarios?

The calculation assumes constant drag coefficient (valid for moderate to high Reynolds numbers, typical of most falling objects). Real-world complications include: varying density with altitude, non-spherical shapes tumbling, air temperature effects, and humidity effects on water drops. The simple formula works well for accurate predictions of skydiving, raindrops, and most engineering applications within the lower atmosphere.

Terminal velocity determines fall time for meteorological particles. For small droplets and particles, fall time becomes long enough that Coriolis force (which depends on velocity and latitude) becomes significant in atmospheric models. In large-scale atmospheric flow, understanding fall velocities of precipitation particles is essential for weather prediction and climate modeling.

Physical Basis & References

This calculator applies Drag Force and Newton’s Laws:

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

At terminal velocity: $mg = \frac{1}{2}\rho A C_d v_t^2$ (forces balanced)

Key Physics Principles:

  • Newton’s Second Law - F = ma governs motion
  • Drag Force - $F_d = \frac{1}{2}\rho A C_d v^2$ (quadratic with velocity)
  • Force Balance - Zero acceleration when gravity equals drag
  • Velocity Dependence - Drag increases with v², enabling terminal velocity

Key Assumptions:

  • Constant drag coefficient (valid for turbulent flow, high Reynolds number)
  • Uniform fluid density (neglecting altitude variation)
  • Rigid, non-rotating object
  • No buoyancy effects
  • Steady-state conditions

Typical Range of Values:

  • Falling object mass: 0.1 kg to 100 kg
  • Projected area: 0.01 to 10 m²
  • Drag coefficient: 0.05 (streamlined) to 1.5 (parachute)
  • Terminal velocity: 1 m/s (feather with parachute) to 90 m/s (compact object)
  • Fluid density: 1.2 kg/m³ (air), 1000 kg/m³ (water)

Further Reading:

  • Goldstein, H. (1980). Classical Mechanics, 2nd Edition. Addison-Wesley.
  • White, F.M. (2011). Fluid Mechanics, 7th Edition. McGraw-Hill.
  • Aerodynamics and Drag - NASA Educational Resources