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Terminal Velocity Calculator

Determine the maximum velocity achievable by a falling object using the terminal velocity calculator.

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Terminal velocity42.7763 m/s153.99 km/h, 95.69 mph
Drag area (Cd × A)0.7 m²the product is what matters — shape and size only enter through it
Weight, and drag at terminal velocity784.532 Nequal by definition — that balance is what "terminal" means
Speed after 10 s41.9122 m/s97.98% of terminal velocity
Distance fallen300.324 m
Speed if drag were ignored98.0665 m/s2.34× the real figure — the drag-free result is unbounded and diverges without limit
Distance if drag were ignored490.333 m190.01 m further
Characteristic time v_t ÷ g4.362 safter this long the fall is at tanh(1) = 76% of terminal velocity
After 4.362 s32.5782 m/s76% of terminal velocity
After 8.724 s41.2375 m/s96% of terminal velocity
After 13.086 s42.5648 m/s99.5% of terminal velocity
At four times the mass85.5526 m/sonly double — terminal velocity goes as the square root of mass, which is why a heavy object falls faster but not proportionally so
At a quarter of the air density85.5526 m/sdouble again — thin air at altitude raises terminal velocity substantially

The formula

v_t = √(2mg ÷ ρACd); v(t) = v_t tanh(gt ÷ v_t)

Why heavy things fall faster in air

In a vacuum every object falls identically. In air, drag grows with the square of speed until it balances weight, and the speed at which that happens is the terminal velocity. It depends on mass divided by drag area, so a dense compact object reaches a far higher terminal velocity than a light bulky one — this, not gravity, is why a stone beats a feather.

The dependence is a square root, though. Four times the mass gives only twice the terminal velocity, which is why the difference between a 70 kg and a 100 kg skydiver is modest.

The approach to terminal velocity is a hyperbolic tangent, not a straight line: about 76% after one characteristic time, 96% after two, and effectively there after three. Using the drag-free ½gt² for anything longer than a couple of seconds is badly wrong — and unlike the real fall, it has no upper bound at all.

Air density falls with altitude, so terminal velocity rises with it. This is how high-altitude jumps reach speeds several times the low-level figure while experiencing no more drag force.