Calculate terminal velocity v_t = √(2mg/ρCdA) for objects falling through fluids. Skydiver, raindrop, and sports ball presets included.
Terminal velocity is the maximum speed a falling object reaches when the drag force equals its weight. At this point, the net force is zero and the object stops accelerating, continuing to fall at a constant speed. The formula v_t = √(2mg/ρCdA) balances gravitational force against aerodynamic drag.
This calculator computes terminal velocity for any object in any fluid. A built-in database covers fascinating real-world examples — from a skydiver in spread position (about 200 km/h) to a head-down dive (over 300 km/h), raindrops of various sizes, and sports balls. You can also switch the fluid medium from air at sea level to higher altitudes or even water for sinking objects.
The velocity-time chart shows the exponential approach to terminal velocity, characterized by the time constant τ = v_t/g. After about 3τ, the object reaches 99% of its terminal speed. The object comparison table lets you rank different objects by their terminal velocity in your selected fluid.
Terminal velocity calculations are essential in aerodynamic design, parachute sizing, atmospheric science (raindrop physics), sports engineering (ball trajectory), and even forensic science (analyzing falls). This calculator handles the full range from microscopic particles to skydivers.
The velocity-time chart provides physical insight into the approach to terminal velocity — showing that most of the acceleration happens in the first few seconds, with the object asymptotically approaching v_t.
Terminal Velocity: v_t = √(2mg / ρCdA) Where: • v_t = terminal velocity (m/s) • m = mass (kg) • g = 9.81 m/s² • ρ = fluid density (kg/m³) • Cd = drag coefficient (dimensionless) • A = cross-sectional area (m²) Time constant: τ = v_t / g Velocity at time t: v(t) = v_t × tanh(gt/v_t)
Result: 50.5 m/s (182 km/h)
v_t = √(2 × 80 × 9.81 / (1.225 × 1.0 × 0.7)) = √(1569.6 / 0.8575) = √(1830.8) ≈ 50.5 m/s ≈ 182 km/h.
As an object moves through a fluid, it must push the fluid aside and create a wake behind it. This requires energy, which manifests as a drag force opposing the motion. At low speeds (Stokes flow), drag is proportional to velocity. At higher speeds (the regime relevant to most everyday objects), drag is proportional to velocity squared — this is the quadratic drag law used in this calculator.
Felix Baumgartner's 2012 stratospheric jump from 39 km altitude demonstrated how dramatically air density affects terminal velocity. In the near-vacuum at jump altitude, he briefly exceeded the speed of sound before decelerating as the air thickened. Alan Eustace broke the altitude record in 2014 (41.4 km) but used a drogue chute that limited his maximum speed.
Parachute designers use terminal velocity calculations to size canopies for specific load weights and descent rates. Hailstone terminal velocity determines impact energy and damage potential. In chemical engineering, terminal velocity of particles in fluidized beds determines reactor design. Environmental engineers use particle settling velocity to design sedimentation basins for water treatment.
Head-down diving reduces both the drag coefficient (more streamlined) and the cross-sectional area exposed to airflow. Both changes decrease drag force, allowing higher terminal velocity.
No. Larger raindrops have higher terminal velocities because mass increases faster (∝r³) than area (∝r²). A 2mm raindrop falls at about 6 m/s, while a 5mm drop reaches about 9 m/s.
Higher altitude means lower air density, which increases terminal velocity. At 3,000 m elevation, terminal velocity is about 16% higher than at sea level.
Cd is a dimensionless number that quantifies an object's aerodynamic resistance. A sphere has Cd ≈ 0.47, a flat plate perpendicular to flow has Cd ≈ 1.28, and a streamlined body can have Cd < 0.1.
Yes, if there is an initial downward velocity greater than v_t (e.g., thrown downward), or if the object was falling in denser air and enters thinner air. It will decelerate toward the new terminal velocity.
Water is about 800× denser than air, so terminal velocity is much lower. A steel ball bearing sinks through water much more slowly than it would fall through air (at any Cd).