Terminal Velocity Calculator

The Terminal Velocity Calculator determines the maximum speed a falling object reaches when aerodynamic drag equals gravitational force. At terminal velocity, net force is zero and the object stops accelerating, descending at a constant speed determined by its mass, shape, and the surrounding fluid properties.

Terminal velocity is given by the equation: $$v_t = \sqrt{\frac{2mg}{\rho C_d A}}$$ where $$m$$ is mass, $$g$$ is gravitational acceleration, $$\rho$$ is fluid density, $$C_d$$ is the drag coefficient, and $$A$$ is the reference cross-sectional area perpendicular to the flow.

The drag coefficient $$C_d$$ depends on the object's shape and the Reynolds number of the flow. A sphere has $$C_d \approx 0.47$$, a flat plate perpendicular to flow has $$C_d \approx 1.17$$, and a streamlined body can have $$C_d \approx 0.04$$. A skydiver in belly-down position has $$C_d \approx 1.0$$ with cross-sectional area around 0.7 m², while in a head-down dive the area drops to about 0.15 m², dramatically increasing terminal velocity.

Air density varies significantly with altitude: at sea level $$\rho \approx 1.225\,\text{kg/m}^3$$, but at 4,000 m altitude it drops to about 0.82 kg/m³. This means terminal velocity increases at higher altitudes—Felix Baumgartner reached supersonic speeds during his 2012 stratospheric jump partly because the near-vacuum upper atmosphere provided negligible drag initially.

The concept extends beyond skydivers to raindrops (terminal velocity 1–9 m/s depending on size), hailstones, parachute design, seed dispersal, volcanic ash fallout, and sedimentation in fluids. Engineers use terminal velocity calculations in designing aerodynamic vehicles, ballistic trajectories, and industrial settling tanks for particle separation.

This calculator assumes the standard drag equation valid for high Reynolds number flow. For very small particles (dust, fog droplets) where Reynolds numbers are below 1, Stokes' law applies instead: $$v_t = 2r^2 g(\rho_p - \rho_f) / (9\mu)$$, which is proportional to radius squared rather than mass.