Head-to-head
Terminal Velocity vs Free Fall
Free fall assumes gravity is the only force. Acceleration is constant at 9.81 metres per second squared, speed rises without limit, and the distance fallen is half of g times t squared. It is a good model for the first second of a fall and an exact one in a vacuum.
Terminal velocity assumes the opposite: that drag grows with the square of speed until it balances weight. At that point the net force is zero, acceleration stops, and the speed stops changing. The object keeps falling, but it no longer gets faster.
The two are the same physics with one term added, and the addition changes the shape of the answer completely. Under free fall the distance to a given speed is short and fixed. With drag it is longer, it depends on mass, area and shape, and the speed is approached asymptotically rather than reached. A 75 kg skydiver at 41.4 m/s has fallen 87 m in a vacuum and 404 m in air. Drag does not change where the object ends up, only how fast it gets there and how hard it lands when it arrives.
Terminal velocity
How To Calculate Terminal Velocity
A falling object stops accelerating when the air pushing up matches its weight. Terminal velocity is the speed where those two forces balance.
Free fall
How To Calculate Free Fall
Free fall is what an object does when gravity is the only force acting on it. Air resistance is ignored, which makes the mathematics exact and the answers a good approximation for anything dense.
How They Differ
| Attribute | Terminal velocity | Free fall |
|---|---|---|
| Forces considered | Gravity only | Gravity and drag |
| Acceleration | Constant 9.81 m/s² | Falls to zero as speed rises |
| Speed over time | Rises without limit | Approaches a fixed value |
| Distance to 41.4 m/s | 87 m | 404 m, for 95% of it |
| Time to 41.4 m/s | 4.22 s | 12.7 s, for 95% of it |
| Depends on mass | No | Yes — heavier falls faster |
| Depends on shape | No | Yes — drag coefficient and area |
| Valid for | The first second, or a vacuum | Any long fall through a fluid |
| Used for | Drop height and impact speed in vacuum | Skydiving, parachutes, falling debris |
| What stops the acceleration | Nothing — the ground does | Drag, well before the ground |
The Same Numbers, Both Ways
A 75 kg skydiver in a spread-eagle position — 0.7 square metres of area and a drag coefficient of 1.0 — falling through air at 1.225 kg per cubic metre.
- Mass
- 75 kg
- Frontal area
- 0.7 m²
- Drag coefficient
- 1.0
- Air density
- 1.225 kg/m³
- Gravity
- 9.81 m/s²
| Line | Terminal velocity | Free fall |
|---|---|---|
| Speed after 4.22 s | 41.43 m/s | 31.55 m/s |
| Distance after 4.22 s | 87.46 m | 75.88 m |
| Speed after 12.67 s | 124.28 m/s | 41.22 m/s |
| Distance after 12.67 s | 787.17 m | 403.96 m |
| Ultimate speed | No limit | 41.43 m/s |
Terminal velocity for this skydiver is 41.43 m/s — 149.1 km/h. In a vacuum that speed arrives after 4.22 s and 87.46 m. With drag the same 4.22 s yields only 31.55 m/s, and reaching 95% of terminal speed takes 12.67 s and 403.96 m. The free-fall model is not wrong; it is answering a question about a fall that has no air in it.
When To Use Each
Terminal velocity
- You are sizing a parachute, where the entire point is to bring terminal speed down to a survivable one.
- You are estimating the impact of hail, debris or a dropped object over a long fall.
- The fall is long enough for drag to matter — roughly more than 100 m for a person.
Free fall
- You are calculating drop height, fall time or impact speed over a short drop where drag is negligible.
- You are working in a vacuum, or in a problem that explicitly ignores air resistance.
- You need the speed after a known time and nothing more.
Common Questions
Does a heavier object fall faster?
In air, yes. Terminal velocity goes as the square root of mass over area, so doubling the mass raises terminal speed by about 41%. In a vacuum, no: every mass accelerates at the same rate, which is what Galileo's experiment was about.
How long does it take to reach terminal velocity?
Practically, about three time constants, where the time constant is terminal velocity divided by g. For a skydiver that is roughly 4.2 s per constant, so about 12.7 s and 400 m of falling. It is an asymptote, so it is never exactly reached.
Why does a parachute work?
It increases area by a factor of about fifty, which cuts terminal velocity by the square root of that — roughly a factor of seven. A 41 m/s fall becomes a 6 m/s one, which is the difference between a fatal impact and a hard landing.
Is terminal velocity constant during a fall?
Only after the transient. Air density falls with altitude, so a fall from 30 km has a far higher terminal velocity at the top than near the ground, and the object decelerates as it descends into thicker air. Felix Baumgartner reached about 377 m/s for exactly that reason.
What drag coefficient should I use for a person?
Around 1.0 spread-eagle and roughly 0.7 head-down, with the frontal area also dropping. That is why the same skydiver falls at about 41 m/s in a spread-eagle position and somewhere between 50 and 60 m/s head-down.
More Comparisons
- Kinetic Energy vs Potential Energy
Kinetic energy comes from motion; gravitational potential energy comes from height. A 10 kg mass 5 m up holds 490.33 J, and hitting the ground at 9.9 m/s it carries the same 490.33 J — the interchange is the whole of a pendulum.
- Momentum vs Impulse
Momentum is the quantity of motion a body carries; impulse is the force-time product that changes it. A 1,500 kg car at 20 m/s carries 30,000 kg m/s, and stopping it takes exactly that much impulse in the other direction.
- Molarity vs Dilution
To make 500 mL of 0.25 M from a 2.0 M stock you need 62.5 mL of stock and 437.5 mL of water — and the dilution factor is 8. Molarity says how strong a solution is; dilution says how to get there.
Sources
- Terminal velocity — the drag balance — NASA Glenn Research Center
- Terminal velocity — derivation and values — Wikipedia
- Free fall — motion under gravity alone — Wikipedia
Both methods sit in Science.