Terminal velocity depends on five main factors: the object’s weight, its cross-sectional area, its shape, the density of the fluid it’s falling through, and its surface texture. Change any one of these and the terminal speed changes. The relationship is captured in a straightforward equation from physics, and understanding each variable helps explain why a skydiver falls faster head-down than belly-down, or why a raindrop and a bowling ball behave so differently in freefall.
The Terminal Velocity Equation
Terminal velocity is the speed at which the drag force pushing up on a falling object exactly equals the gravitational force pulling it down. Once those forces balance, acceleration stops and the object falls at a constant speed. NASA’s aeronautics reference expresses this as:
V = √(2W / (Cd × ρ × A))
In that formula, V is terminal velocity, W is the object’s weight, Cd is the drag coefficient (a number representing shape and surface effects), ρ is the density of the fluid (air, water, etc.), and A is the reference area the object presents to the oncoming flow. Every factor that affects terminal velocity shows up in this equation, so it’s worth walking through each one.
Weight: Heavier Objects Fall Faster
Weight sits in the numerator of the equation, which means a heavier object has a higher terminal velocity, all else being equal. This is why a lead ball falls faster than a plastic ball of the same size. The heavier object needs more drag force to counterbalance gravity, and the only way to generate more drag is to move faster through the fluid.
What matters practically is the ratio of weight to area. A large, lightweight object like a parachute has very little weight relative to the huge area it presents to the air, so its terminal velocity is low. A small, dense object like a bullet has a lot of weight packed into a tiny cross-section, so it falls fast. This ratio is sometimes called the ballistic coefficient, and it’s one of the most influential factors in real-world terminal velocity problems.
Cross-Sectional Area
The reference area (A) in the equation is the size of the “shadow” an object casts in the direction of motion. A larger area means more air molecules are being displaced, creating more drag at any given speed, which brings the object to terminal velocity sooner and at a lower speed.
Skydivers demonstrate this clearly. In a stable belly-to-earth position, a human body reaches a terminal velocity of about 200 km/h (120 mph). Rotate into a vertical head-down position, which cuts the area exposed to the airflow roughly in half, and terminal velocity jumps to 240–290 km/h (150–180 mph). Same weight, same atmosphere, but a dramatic speed difference driven almost entirely by area and body orientation.
Shape and the Drag Coefficient
The drag coefficient (Cd) is a dimensionless number that captures how “slippery” or “blunt” a shape is as it moves through a fluid. It accounts for the complex way air flows around curves, edges, and trailing surfaces. A higher Cd means the shape generates more drag for its size, resulting in a lower terminal velocity.
NASA provides some reference values that illustrate the range. A flat plate perpendicular to the flow has a Cd of 1.28, meaning it catches nearly as much drag as geometry allows. A sphere ranges from about 0.07 to 0.5, depending on speed and surface conditions. A streamlined airfoil shape has a Cd of just 0.045, roughly 28 times less draggy than a flat plate. That’s why teardrops and bullet shapes fall much faster than flat or angular objects of the same weight and size.
Shape matters so much that engineers spend enormous effort on streamlining. The difference between a Cd of 0.5 and 0.07 for a sphere alone translates to a terminal velocity roughly 2.7 times higher at the lower drag coefficient.
Surface Roughness
Surface texture affects the drag coefficient in ways that aren’t always intuitive. A rough surface disrupts the thin layer of air flowing directly over the object (the boundary layer), which changes how much drag the object experiences. In some cases, roughness increases drag. In others, it can actually decrease it by changing the way airflow separates from the surface.
Research on turbulent boundary layers shows that drag from surface roughness peaks at a specific coverage level, around 30% of the surface area, and then gradually decreases as more roughness is added. This counterintuitive result happens because densely packed roughness elements start to “shelter” each other from the flow. For a golf ball, the dimples (a controlled form of roughness) trip the boundary layer into turbulence, which delays flow separation and reduces overall drag compared to a smooth ball. This is why a golf ball actually travels farther than a smooth sphere of the same size would.
For most falling objects, though, increased roughness means increased drag and a lower terminal velocity.
Fluid Density
The density of the fluid (ρ) appears in the denominator of the terminal velocity equation, so denser fluids produce lower terminal velocities. This is why a marble sinks slowly through honey but falls quickly through air. The thicker the surrounding medium, the more drag force it generates at any given speed.
Even within air alone, density varies meaningfully. Air is about 1.225 kg/m³ at sea level but thins out as altitude increases. At 4,000 meters (roughly 13,000 feet, a typical skydiving altitude), air density drops to about 0.82 kg/m³. That roughly 33% reduction in density means a skydiver’s terminal velocity is noticeably higher at altitude than it would be closer to the ground. As the diver falls and enters thicker air, drag increases and terminal velocity gradually decreases, so the diver actually slows down during the final portion of the fall.
Temperature also affects fluid density. Warm air is less dense than cold air, so terminal velocity is slightly higher on a hot day than a cold one at the same altitude.
Terminal Velocity in Liquids
The same basic principles apply when objects sink through water or other liquids, but one additional factor becomes important: buoyancy. In a liquid, the effective weight pulling the object down is reduced by the weight of the fluid it displaces. Physicists call this the “submerged weight,” calculated as the difference between the object’s density and the fluid’s density.
For small particles settling slowly through viscous fluids (at very low speeds where the flow stays smooth), terminal velocity simplifies to a formula where it’s proportional to the square of the particle’s diameter, the density difference between particle and fluid, and inversely proportional to the fluid’s viscosity. This is why fine silt takes hours to settle in still water, while sand grains drop almost immediately. Double the particle diameter and the settling velocity quadruples.
If an object is less dense than the surrounding fluid, the physics works in reverse. Instead of sinking, the object rises until it reaches a terminal velocity upward. This is how air bubbles behave in water and weather balloons behave in the atmosphere.
Gravity’s Role
Gravity determines the weight (W) in the equation since weight equals mass times gravitational acceleration. On Earth, gravity varies slightly by location, from about 9.78 m/s² at the equator to 9.83 m/s² at the poles, due to the planet’s rotation and shape. This creates a small but real difference in terminal velocity depending on latitude.
The effect becomes dramatic on other planets. Mars has about 38% of Earth’s surface gravity, so an object’s weight there is much lower. With less gravitational pull and a very thin atmosphere (about 1% of Earth’s air density at the surface), terminal velocities on Mars are far higher than on Earth for the same object. This is one reason landing spacecraft on Mars is so challenging: parachutes are far less effective when the atmosphere is thin and the terminal speeds are high.