Free Fall with Air Resistance Calculator

Free fall with air resistance calculator finds the time of fall, as well as the maximum and terminal velocity of an object falling to the ground under the influence of both gravity and air resistance.

Speed after 30 s42.7762 m/s100% of terminal velocity

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

Distance fallen1,153.956 m

Speed if drag were ignored294.1995 m/s6.88× the real figure — the drag-free result is unbounded and diverges without limit

Distance if drag were ignored4,412.993 m3,259.04 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.