What your result means
Terminal velocity is the speed at which drag has grown to exactly cancel weight, so the fall stops accelerating. Impact speed is how fast the object is actually travelling when it arrives — which is only equal to terminal velocity if the drop was long enough to get there.
Share of terminal reads that as a percentage, and it is the number worth watching: on short drops it stays low and drag barely matters, while on long ones it pins at 100% and the extra height buys no extra speed at all. The energy arriving with the object at that speed is what the kinetic energy calculator converts into joules.
Why this one is different
Impact speed is reported next to terminal velocity as a percentage of it, which is the number that tells you whether the drop was long enough for air resistance to matter at all. Fall time comes with them, and a plain-English line reads the three together instead of leaving three figures to be interpreted.
How it works
Two forces act. Weight is constant — mass times gravity — and pulls down. Drag pushes up and grows with the square of speed, so it starts at nothing and strengthens rapidly as the fall builds. Early on, weight dominates and the object accelerates at very nearly the full 9.81 m/s². As speed rises, drag closes the gap, acceleration fades, and the speed curve bends over onto a flat line.
Because drag depends on the square of speed, this simulator does not need to guess its way forward: the equation has an exact solution built from the hyperbolic tangent, which is the shape you see traced on the graph. Note what does and does not appear in the terminal velocity formula — mass and size do, but drop height does not. Height only decides how much of the curve you get to see. Whether the flow is smooth enough for a single drag coefficient to apply is a question for the Reynolds number calculator.
How to use this simulator
- Set the mass and the frontal area — the silhouette the air actually meets, not the total surface.
- Pick a shape to set the drag coefficient. Flat plate and streamlined body are the two extremes.
- Set the drop height, then press play and watch the graph flatten.
- Try 1 m and then 1000 m at the same settings: impact speed barely changes above a few hundred metres, because the object is already at terminal velocity.
Long drops are played back faster than real time so the whole fall fits in a few seconds; the stage shows the multiplier, and every number reported is the real-world one.
Formula
terminal velocity: vₜ = √( 2 m g ÷ ( ρ · Cᵈ · A ) )
speed at time t: v = vₜ · tanh( g t ÷ vₜ )
impact speed: v = vₜ · √( 1 − e^( −2 g h ÷ vₜ² ) )
fall time: t = ( vₜ ÷ g ) · arcosh( e^( g h ÷ vₜ² ) )
- m — mass of the falling object, in kilograms
- A — frontal area presented to the airflow, in m²
- Cᵈ — drag coefficient, a dimensionless number set by shape
- ρ — air density, 1.225 kg/m³ at sea level
- g — gravitational field strength, 9.80665 m/s²
- h — drop height, in metres, measured from release to impact
Example calculation
An 80 kg skydiver, spread-eagled at 0.7 m² and Cᵈ 1.0, dropped from 1000 m:
v = 42.78 × √( 1 − e^( −2 × 9.80665 × 1000 ÷ 42.78² ) ) = 42.78 m/s
t = ( 42.78 ÷ 9.80665 ) × arcosh( e^( 9.80665 × 1000 ÷ 42.78² ) ) = 26.40 s
share of terminal = 100.0 %
Set the controls to those values and the panel shows the same figures. With no air at all the same drop would end at 140.05 m/s after only 14.28 s — more than three times the speed, and drag is the entire difference.
Terminal velocities to compare against
All four computed with this tool's own model, treating drops and hailstones as spheres (Cᵈ 0.47) and the head-down body as 0.18 m² at Cᵈ 0.7. The same 80 kg body more than doubles its speed simply by presenting a smaller silhouette.
Frequently asked questions
Do heavy objects fall faster than light ones?
In a vacuum, no. With air, yes, because terminal velocity rises with the square root of mass while drag depends only on size and shape. Double the mass of an object without changing its shape and its terminal velocity rises by about 41 percent. That is why a hammer beats a feather in air but ties with it on the Moon.
How long does it take to reach terminal velocity?
Strictly, never. Speed approaches terminal velocity asymptotically, getting closer without arriving. A useful measure is the time to reach 95 percent of it, which is about 8 seconds for a spread-eagled skydiver and only a fraction of a second for a raindrop. Small light objects settle into their final speed almost immediately.
Why is the no-air answer so much larger?
Without drag, speed grows without limit as long as the fall continues, so a 1000 metre drop ends at about 140 metres per second. With air, the fall levels off at terminal velocity and stays there, which for a typical skydiver is around 43 metres per second. The longer the drop, the wider the gap between the two answers.
Related calculators
Assumptions & limitations
- The drag coefficient is constant. In reality it shifts with speed — a smooth sphere's drops sharply once the boundary layer turns turbulent.
- Air density does not change with altitude. Above a couple of thousand metres air thins, terminal velocity rises, and high-altitude jumps go much faster than this model says.
- The object starts from rest and keeps its shape. No initial throw, no tumbling, no parachute deploying part-way down.
- Still air. No wind, updraughts or thermals, and no lift — the fall is straight down.
- Gravity is uniform. Fixed at 9.80665 m/s², which is fine for any drop short enough to happen inside the atmosphere.
Further reading
Our guide to force, work, energy and power covers the balance between weight and drag that sets the terminal speed.
Sources & references
The drag equation, the drag coefficients and the constants used here come from the following, all specific to falling bodies in air.
- NASA Glenn Research Center — the drag equation, and the definition of the drag coefficient
- NASA Glenn Research Center — shape effects on drag, the source of the Cᵈ values in the shape list
- NIST — standard acceleration of gravity, the exact 9.80665 m/s² used here
- ISO 2533, Standard Atmosphere — sea-level air density of 1.225 kg/m³ at 15 °C