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Terminal Velocity Calculator

Calculate the terminal (maximum falling) velocity of an object from its mass, cross-sectional area, drag coefficient, and air density.

Terminal velocity
42.78 m/s
Terminal velocity (mph)
95.7 mph
Terminal velocity (km/h)
154.02 km/h

How it works

A falling object accelerates until drag force exactly balances its weight, at which point it stops speeding up — that constant speed is the terminal velocity. Setting the standard drag-force equation ½ × air density × v² × Cd × area equal to weight (mass × gravity) and solving for v gives v = √((2 × mass × gravity) ÷ (air density × Cd × area)). Verified via web search against HyperPhysics's 'Terminal Velocity' reference and the University Physics (OpenStax) 'Drag Force and Terminal Speed' chapter, reproducing their own worked examples: an 80kg skydiver (Cd 1.0, 0.7m² presented area, 1.2kg/m³ air) settles at about 43.2 m/s, and the same skydiver presenting a smaller 0.5m² area at sea-level air density settles at about 50.6 m/s.

Mass, cross-sectional area, and gravity get this page's metric/imperial toggle, converted to kilograms, square meters, and meters per second squared (the units the drag equation is published in) before the formula runs. Gravity defaults to Earth's standard 9.81 m/s² but is a normal, editable input — change it to the Moon's ~1.62 or Mars' ~3.71 m/s² to see how much slower an equivalent fall would terminate elsewhere. Air density and the drag coefficient are left as plain, un-toggled inputs, since kg/m³ and a dimensionless shape factor are already the standard units used worldwide in aerodynamics.

FAQ

What drag coefficient should I use?

It depends entirely on shape, and is something you supply rather than something this calculator can assume: a flat plate facing the airflow broadside is around 1.0-1.3, a skydiver in a belly-to-earth 'stable' position is commonly cited near 1.0, a sphere is close to 0.5, and a deployed parachute canopy is roughly 1.5-2.2. These are reference points, not fixed facts — the true value for a specific real object usually comes from wind-tunnel testing.

Does reaching terminal velocity mean the object stops accelerating instantly?

No — terminal velocity is the speed an object approaches over time, not one it reaches the instant it starts falling. Acceleration is highest at the start (when speed, and therefore drag, is lowest) and shrinks continuously as speed builds and drag grows toward matching weight; in practice, most of that approach happens within the first several seconds for something like a skydiver, but it's asymptotic rather than sudden.

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