Terminal Velocity Calculator

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.