Terminal Velocity Calculator: Maximum Falling Speed

Terminal velocity is the maximum speed an object reaches when falling through air, reached when drag force equals gravitational force. A skydiver in free fall accelerates initially, but air resistance increases with speed until reaching an equilibrium — no net force means no further acceleration. This balance is terminal velocity.

The Formula

Terminal Velocity = √((2 × m × g) / (ρ × A × Cd))

Where:

• m = mass of object (kg)
• g = gravitational acceleration (9.81 m/s²)
• ρ (rho) = air density (1.225 kg/m³ at sea level)
• A = cross-sectional area (m²)
• Cd = drag coefficient (dimensionless, ~0.5-1.5 for most objects)

Terminal velocity increases with mass and decreases with drag coefficient and cross-sectional area.

Worked Example

A skydiver: mass 80 kg (including gear), cross-sectional area 0.5 m² (in spread position), drag coefficient ~1.1

Terminal Velocity = √((2 × 80 × 9.81) / (1.225 × 0.5 × 1.1))
                  = √(1,569.6 / 0.67375)
                  = √(2,329)
                  = 48.3 m/s ≈ 174 km/h (108 mph)

In a head-down position (smaller area, Cd ~0.7):

Terminal Velocity = √((2 × 80 × 9.81) / (1.225 × 0.2 × 0.7))
                  = √(1,569.6 / 0.1715)
                  = √(9,143)
                  = 95.6 m/s ≈ 344 km/h (214 mph)

Position dramatically affects terminal velocity.

Drag Coefficient Values

More aerodynamic shapes have lower drag coefficients.

Real-World Factors

Air density decreases with altitude, so terminal velocity changes with height. At cruising altitude (11 km), air is 1/3 as dense, so terminal velocity is √3 ≈ 1.73× higher. This is why skydive planes reach higher speeds at altitude.

Tips

Terminal velocity is reached relatively quickly — most objects achieve it within seconds or meters. For physics problems, assume constant velocity once terminal velocity is reached. Also remember this only applies to vertical or near-vertical motion; angled descent is more complex.

Use our Terminal Velocity Calculator to find terminal velocity for any mass, size, and drag coefficient.