Terminal velocity: the steady speed (vt) an object reaches when falling through a fluid, where drag exactly balances weight — given by vt = √(2mg / ρACd). This free calculator solves for terminal velocity or mass and shows every step of the working.
When an object falls through a fluid such as air or water, gravity pulls it down while aerodynamic drag pushes back up. Drag grows with the square of speed, so as the object speeds up the drag force rises until it exactly cancels the object’s weight. From that moment the net force is zero, the object stops accelerating, and it falls at a constant terminal velocity.
To find it, set weight equal to the drag force mg = ½·ρ·v²·A·C_d and rearrange for speed: v_t = √(2·m·g / (ρ·A·C_d)). Here m is the mass, g is the acceleration due to gravity (9.80665 m/s²), ρ is the fluid density, A is the cross-sectional area facing the flow, and C_d is the dimensionless drag coefficient that captures the object’s shape.
There are three steps. First, choose whether you want terminal velocity or mass in the Solve for menu. Second, enter the values you know and pick their units; the calculator converts everything to SI base units (kilograms, metres, m/s) automatically, and offers presets for common fluids and shapes. Third, read the answer alongside the worked steps showing the formula, your numbers substituted in, and the result with units.
The relationship explains a lot about falling. Terminal velocity rises with the square root of mass and falls with the square root of density and area — which is why a skydiver slows down by spreading out, and why the same body falls faster in thin, high-altitude air. For falling motion before drag becomes important, see the free-fall calculator; for a deeper walkthrough of the physics, read our guide on terminal velocity.
A skydiver of mass m = 80 kg falls belly-down with a cross-sectional area A = 0.7 m² and drag coefficient C_d = 1.0 through sea-level air (ρ = 1.225 kg/m³). The terminal velocity is v_t = √(2·80·9.80665 / (1.225·0.7·1.0)) = √(1829.8) ≈ 42.8 m/s, or about 154 km/h. Tucking into a head-down dive halves the area and the drag coefficient, pushing the terminal velocity past 80 m/s.
Terminal velocity governs how fast raindrops, hailstones, parachutists and spacecraft debris fall, and it sets the limits for safe skydiving, parachute design, sediment settling in water, and the calibration of wind tunnels — anywhere drag and gravity reach a balance.
Terminal velocity is the constant speed an object reaches while falling through a fluid when the upward drag force exactly balances the downward pull of gravity. At that point the net force is zero, so the object stops accelerating and falls at a steady rate.
Terminal velocity is v_t = √(2mg / (ρ·A·C_d)), where m is mass, g is the acceleration due to gravity (9.80665 m/s²), ρ is the fluid density, A is the cross-sectional area facing the flow, and C_d is the drag coefficient. It comes from setting weight equal to the quadratic drag force ½ρv²·A·C_d.
A skydiver falling belly-to-earth reaches roughly 50–55 m/s (about 180–200 km/h) in the lower atmosphere. Diving head-first reduces the cross-sectional area and drag coefficient, so the terminal velocity rises to around 90 m/s or more. The exact value depends on body position, mass and altitude.
Terminal velocity grows with the square root of mass: doubling the mass raises it by about 41%. A heavier object needs a larger drag force to balance its greater weight, and since drag rises with speed, it must fall faster before drag catches up. Shape and area matter just as much, which is why a feather and a coin of equal mass still fall differently.
Yes. Air density (ρ) falls as altitude increases, and terminal velocity is inversely proportional to the square root of density. Thin high-altitude air therefore allows much higher terminal velocities, which is how record free-fall jumps from the stratosphere reach supersonic speeds before slowing in the denser air below.