Terminal Velocity Calculator

Terminal velocity is the constant speed a falling object approaches when the upward drag force equals its downward weight. Once those forces balance, net force and acceleration become zero, although the object continues moving. This calculator uses the familiar quadratic drag equation vₜ = √(2mg/(ρCₐA)). Here m is mass, g is gravitational acceleration, ρ is fluid density, Cₐ is the dimensionless drag coefficient, and A is the projected cross-sectional area perpendicular to motion. The equation is most useful for objects moving fast enough through air or another fluid that drag is approximately proportional to speed squared. Larger mass or stronger gravity increases terminal speed. Greater fluid density, drag coefficient, or frontal area increases resistance and lowers terminal speed. Shape and orientation therefore matter greatly: a spread-out skydiver has a larger area and usually a larger drag coefficient than the same person in a streamlined dive. Drag coefficient is not a universal material property. It depends on geometry, surface roughness, orientation, Reynolds number, and flow conditions. Typical approximate values include about 0.47 for a smooth sphere and roughly 1.0 to 1.3 for broad bluff bodies, but a precise engineering analysis should use experimental or validated reference data. Cross-sectional area must be the area presented to the flow rather than total surface area. At standard sea-level conditions near 15 °C, dry-air density is about 1.225 kg/m³; density decreases with altitude and changes with temperature and pressure. This ideal model assumes a constant fluid density, constant drag coefficient, no wind, and enough falling distance for a steady speed to develop. It does not calculate the time or distance needed to approach terminal velocity. It also ignores buoyancy, which is often negligible for dense objects in air but can matter in liquids or for low-density bodies. For safety-critical aerospace, sporting, or engineering work, treat the result as an estimate and use a full trajectory model, appropriate uncertainty margins, and verified physical data.