Terminal Velocity Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
Terminal velocity is calculated with v = √((2 × mass × g) ÷ (fluid density × area × Cd)). A baseball in free fall through air reaches a terminal velocity of about 33.3 m/s (about 120 km/h).
Explanation
Unlike an idealized free fall in a vacuum, where an object accelerates indefinitely under gravity, an object falling through air encounters growing resistance as its speed increases, called aerodynamic drag. This drag opposes the object's weight and grows with the square of velocity: at some point it becomes exactly equal to the weight, and the object stops accelerating — this equilibrium speed is the terminal velocity. Four factors determine this speed: a higher mass increases terminal velocity (more weight to counterbalance), while a larger frontal area, a denser fluid (see our density calculator for this quantity), or a higher drag coefficient (a less aerodynamic shape) all reduce it, by increasing the resistance encountered. This is the principle that explains why a skydiver in free fall, arms and legs spread to maximize surface area and drag, reaches a terminal velocity on the order of 190-200 km/h, while the same skydiver with an open parachute (considerably larger surface, much higher drag coefficient) sees their terminal velocity drop to just a few meters per second, allowing a safe landing.
Example: a baseball in free fall through air
Inputs
Mass: 0.145 kg. Air density: 1.225 kg/m³. Frontal area: 0.0042 m². Drag coefficient: 0.5 (sphere).
Calculation
v = √((2 × 0.145 × 9.81) ÷ (1.225 × 0.0042 × 0.5)) = √(2.845 ÷ 0.002573) ≈ √1106 ≈ 33.26 m/s.
Result
This baseball reaches a terminal velocity of about 33.3 m/s, or about 120 km/h.
Frequently asked questions
Why does a parachute reduce terminal velocity so much?
Because it considerably increases both the frontal area exposed to the wind (a deployed parachute covers a much larger surface than the body alone) and the drag coefficient (its shape is designed to maximize air resistance rather than minimize it). Since both quantities sit in the denominator of the formula, their combined increase drastically reduces terminal velocity, from about 190-200 km/h in free fall to just a few meters per second under an open parachute.
Why don't two objects of different masses but the same shape share the same terminal velocity?
Because terminal velocity depends on the square root of mass, but on the inverse square root of frontal area and drag coefficient: two objects of the same shape but different sizes generally don't have the same mass-to-surface ratio (mass grows with volume, so with the cube of a linear dimension, while frontal area only grows with the square). This is why a large hailstone falls faster than a small one, for the same shape and density.
Does this formula also apply to falling through a liquid?
Yes, the same principle applies to falling through any fluid, including a liquid like water, simply by using that liquid's density instead of air's. Since water's density is about 800 times higher than air's, the terminal velocity of the same object is generally much lower in water. At terminal velocity, this drag force exactly balances the object's weight, calculated by our weight calculator.