Velocity from fall time v = g × t
Enter how long the object has been falling to get its free fall velocity. After 3 seconds on Earth: 29.42 m/s (105.9 km/h).
Velocity from drop height v = sqrt(2 × g × h)
Enter the height the object fell from to get its impact velocity. Dropped from 100 m on Earth: 44.29 m/s (159.4 km/h, 99.1 mph).
Fall time from velocity t = v / g
Know the speed and want the fall duration? Enter the velocity to find how long the object must have been falling.
Drop height from velocity h = v² / (2 × g)
Measured (or estimated) an impact speed? Work backwards to find the height the object must have fallen from.
Fall time from height t = sqrt(2 × h / g)
How long does the fall take? Enter the drop height to get the free fall time. From 100 m on Earth: 4.52 s.
Fall distance from time h = ½ × g × t²
Timed a fall with a stopwatch? Enter the duration to find how far the object dropped. After 8 s on Earth: 313.8 m.
Kinetic energy of a falling object KE = ½ × m × v²
Velocity tells you the speed; energy tells you the punch. Enter mass and impact velocity for the kinetic energy at impact. A 70 kg object at 44.29 m/s carries 68.6 kJ.
Terminal velocity estimator vt = sqrt(2 × m × g / (ρ × A × Cd))
In air, a falling object stops accelerating when drag balances weight. Estimate that cap speed from mass, frontal area, drag coefficient and air density. A belly-to-earth skydiver (80 kg): ≈ 42.8 m/s (154 km/h).
Above this speed the object cannot accelerate further in steady fall — it is the ceiling the vacuum solvers on this page ignore. Real long falls approach it asymptotically.
Free fall speed chart (vacuum)
Velocity and fall time for selected drop heights on Earth (g = 9.80665 m/s²). Note how doubling the height multiplies the speed by only √2 ≈ 1.41 — speed grows with the square root of height.
| Height | Height (ft) | Fall time | Velocity (m/s) | Velocity (km/h) | Velocity (mph) |
|---|
Vacuum values. In air, anything falling more than a few hundred metres hits terminal velocity long before these speeds — e.g. the 4,000 m row's 280 m/s is a vacuum fantasy; a real skydiver caps near 54 m/s.
Famous falls: how fast would you hit?
Vacuum impact speeds for well-known drops. A fun way to feel the numbers — and to see exactly where air resistance takes over.
| Drop | Height | Fall time (vacuum) | Impact velocity (vacuum) | Reality check |
|---|
All free fall formulas in one place
Velocity from time
v = g × t
Linear: every second adds another 9.81 m/s on Earth. After 10 s: 98.07 m/s.
Velocity from height
v = √(2 × g × h)
The impact-velocity workhorse. From 100 m: 44.29 m/s.
Time from velocity
t = v / g
Inverse of v = g×t. Reaching 29.42 m/s takes exactly 3 s.
Height from velocity
h = v² / (2 × g)
Inverse of v = √(2gh). An impact at 44.29 m/s implies a 100 m drop.
Time from height
t = √(2 × h / g)
Falling 100 m takes 4.52 s in a vacuum.
Height from time
h = ½ × g × t²
Quadratic: 8 s of fall covers 313.8 m.
Kinetic energy
KE = ½ × m × v²
Energy at impact scales with velocity squared — the real measure of how hard it hits.
Terminal velocity
vt = √(2 × m × g / (ρ × A × Cd))
The speed cap in air, where drag force equals weight. Not a vacuum formula — it is the vacuum formulas' real-world limit.
Free fall vs terminal velocity
Free fall (this page's solvers) describes an object accelerating under gravity alone — strictly true only in a vacuum. Terminal velocity is what happens in a fluid like air: drag grows with the square of speed until it exactly cancels weight, and acceleration stops.
- Short drops (a few metres): air resistance is negligible; the vacuum formulas are accurate to a few percent for dense objects.
- Long drops (hundreds of metres): the object reaches terminal velocity and the vacuum numbers become pure fantasy — e.g. 280 m/s from 4,000 m vs a skydiver's real ~54 m/s.
- Terminal velocity depends on the object (mass, area, shape) — unlike vacuum free fall, where mass does not matter at all.
- Feather vs bowling ball: in a vacuum they land together (Galileo); in air the feather's huge area-to-mass ratio gives it a tiny terminal velocity.
Use tab 8 above to estimate terminal velocity for any object, or read the FAQ for the full comparison.
Method & assumptions
- Vacuum, no air resistance. Every solver assumes drag = 0 and states it. The terminal velocity estimator is the explicit bridge to reality.
- Dropped from rest. Initial velocity v₀ = 0. Objects thrown downward need v = v₀ + g×t instead.
- Constant g. Gravity is treated as constant over the fall; fine for everyday heights, not for orbital scales.
- Standard gravity 9.80665 m/s² for Earth; planetary values from NASA planetary fact sheets (Moon 1.62, Mars 3.71, Mercury 3.70, Venus 8.87, Jupiter 24.79, Saturn 10.44, Uranus 8.87, Neptune 11.15, Sun 274.0 m/s²).
- Unit factors are exact by definition: 1 m/s = 3.6 km/h; 1 ft = 0.3048 m; 1 mi = 1609.344 m; 1 lb = 0.45359237 kg.
- Educational estimates. Results are physics-idealized values for learning and problem-checking, not engineering or safety data.
Scope boundary: what this tool is (and isn't)
- This tool = VELOCITY. It answers "how fast is it falling?" — free fall velocity from time or height, plus the inverse questions.
- Need DISTANCE? Use the companion free fall distance calculator — it answers "how far did it fall?" (the distance dimension of the same physics).
- Need drag over time? This page gives vacuum trajectories plus a terminal-velocity cap estimate; it does not integrate air drag second-by-second.
- Climbing falls (fall factor, impact force in kN, rope stretch) live in the climbing fall factor lab — a different physics model (elastic rope, not free fall).