Terminal Velocity Calculator
Calculate the terminal velocity of a falling object based on mass, drag coefficient, cross-sectional area, and air density.
Terminal Velocity is the maximum speed an object reaches when falling through a fluid (such as air). At this speed, the drag force equals the gravitational force, so the object stops accelerating.
The formula:
Vt = √(2mg / (ρ × A × Cd))
Where:
- Vt = terminal velocity (m/s or ft/s)
- m = mass of the object (kg or slugs)
- g = acceleration due to gravity (9.81 m/s² or 32.17 ft/s²)
- ρ (rho) = air density (1.225 kg/m³ at sea level, or 0.00238 slugs/ft³)
- A = cross-sectional area perpendicular to the direction of motion (m² or ft²)
- Cd = drag coefficient (dimensionless)
Common drag coefficients:
- Sphere: 0.47
- Flat plate (perpendicular to flow): 1.28
- Cube: 1.05
- Streamlined body: 0.04
- Human (skydiver, belly-down): 1.0
- Human (skydiver, head-down): 0.7
- Parachute: 1.5-2.0
Real-world terminal velocities:
- Skydiver (belly-down): ~120 mph (193 km/h, 54 m/s)
- Skydiver (head-down): ~180 mph (290 km/h, 80 m/s)
- Baseball: ~95 mph (153 km/h, 42 m/s)
- Tennis ball: ~70 mph (113 km/h, 31 m/s)
- Golf ball: ~70 mph (113 km/h, 31 m/s)
- Penny: ~25 mph (40 km/h, 11 m/s)
- Raindrop: ~20 mph (32 km/h, 9 m/s)
- Feather: ~0.5 mph (0.8 km/h, 0.2 m/s)
Air density changes with altitude: At higher altitudes, air is thinner (lower density), so terminal velocity increases. This is why skydivers in high-altitude jumps (like Felix Baumgartner’s space jump in 2012) can exceed 800 mph before the thicker atmosphere at lower altitudes slows them down.
The opposing forces: gravity pulls the object down with force F = mg, while drag pushes back with force Fd = ½ρV²CdA. At terminal velocity, these are equal.