Terminal Velocity
Calculate the terminal velocity of any free-falling object using mass, cross-sectional area, and drag coefficient. Physics-based formula vt = √(2mg/ρACd) with instant results and charts.
About This Calculator
The Terminal Velocity Calculator computes the maximum constant speed a falling object reaches when the upward drag force balances the downward gravitational force. This physics tool is essential for skydivers, engineers, physicists, and students studying fluid dynamics and free-fall motion.
Using the standard drag equation vt = √(2mg/ρACd), the calculator applies sea-level air density (ρ = 1.225 kg/m³) and Earth's gravitational acceleration (g = 9.81 m/s²). The drag coefficient (Cd) varies by shape — a streamlined body like a peregrine falcon has Cd ≈ 0.5, while a flat plate perpendicular to flow has Cd ≈ 1.28. For reference, a human skydiver (belly-to-earth, mass 75 kg, area 0.18 m², Cd 0.7) achieves a terminal velocity of approximately 98 m/s (353 km/h or 219 mph).
Real-world applications include parachute design, sports engineering (cycling helmets, ski suits), automotive aerodynamics, industrial particle separation, and meteorology (raindrop fall speed). The results are most accurate at low altitudes (sea level to ~5,000 m) where standard air density holds. For high-altitude jumps or different fluid media (water, oil), adjust the density and gravity constants accordingly.
How to Use This Calculator
Enter the object's mass in kilograms, its cross-sectional area perpendicular to the direction of motion in square meters, and the drag coefficient. Click Calculate to instantly see terminal velocity in both m/s and km/h. The breakdown table displays each input value alongside the computed results for easy verification of the formula steps.
Frequently Asked Questions
What is terminal velocity?
Terminal velocity is the constant maximum speed a falling object reaches when the downward force of gravity is balanced by the upward drag force of the fluid (air or water) it is moving through. At this point, acceleration becomes zero and the object falls at a steady speed.
What factors affect terminal velocity?
Terminal velocity depends on four factors: mass of the object (heavier objects fall faster), cross-sectional area (larger area increases drag and lowers terminal velocity), drag coefficient (streamlined shapes have lower drag), and the density of the fluid (higher density increases drag).
How is terminal velocity calculated?
Terminal velocity is calculated using the formula vt = sqrt(2mg/ρACd), where m is mass in kg, g is gravitational acceleration (9.81 m/s²), ρ is fluid density (1.225 kg/m³ for air at sea level), A is cross-sectional area in m², and Cd is the drag coefficient.
What is the terminal velocity of a skydiver?
A skydiver in a belly-to-earth position (mass 75 kg, area 0.18 m², Cd 0.7) reaches a terminal velocity of about 98 m/s or 353 km/h. When pulling limbs in to reduce area, terminal velocity can increase to over 200 km/h.
Can terminal velocity be exceeded?
An object cannot exceed its terminal velocity through gravity alone. However, if an initial downward force is applied (like a rocket engine or a bullet fired downward), the object can temporarily exceed its terminal velocity until drag slows it back to the equilibrium speed.
Does terminal velocity change with altitude?
Yes, terminal velocity increases at higher altitudes because air density decreases. For example, a skydiver jumping from 40,000 feet experiences lower air density and higher terminal velocity during the initial part of the fall compared to near sea level.
What is the difference between terminal velocity in air and water?
Water is about 800 times denser than air, so terminal velocity in water is much lower than in air. For example, a human in water reaches terminal velocity at around 4-5 m/s, while the same person in air reaches about 55 m/s (belly-to-earth).
How accurate is this calculator for real-world use?
This calculator uses the standard drag equation with sea-level air density (1.225 kg/m³) and Earth gravity (9.81 m/s²). Results are accurate for objects falling at low altitudes where these standard values apply. For high altitudes or different fluids, the constant values should be adjusted.