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)
• m = mass of the object (kg)
• g = acceleration due to gravity, 9.81 m/s²
• ρ (rho) = air density, 1.225 kg/m³ at sea level
• A = cross-sectional area perpendicular to the direction of motion (m²)
• Cd = drag coefficient (dimensionless)

Pick imperial below and the calculator takes pounds and square feet, converts to kilograms and square metres, and works in SI throughout. It does not want slugs. Textbooks that keep the formula in imperial units use slugs for mass, and a pound value entered where a slug is expected is wrong by a factor of 32.2, so it is worth being explicit about which one a tool is asking for.

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

Cd and A only ever appear multiplied together. That product, the drag area, is the only thing the formula cares about, and it is why quoted drag coefficients differ so much between sources: they are paired with different assumed areas. If you plug in 80 kg with 0.7 m² and Cd = 1.0 you get 43 m/s, or 96 mph, not the 120 mph in the table below. Nothing is wrong with either number. The published skydiver figure corresponds to a drag area of about 0.45 m², because a belly-down flyer is not a flat plate and much of that 0.7 m² outline is arm and leg with air spilling around it. Fit the drag area to a speed you trust rather than measuring your silhouette.

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.