Free Fall Calculator
Calculate velocity, distance, and time for objects in free fall under gravity. Works for Earth, Moon, Mars, or any custom gravitational acceleration.
What Is Free Fall?
Free fall is motion under the sole influence of gravity — no air resistance, propulsion, or other forces act on the object. In this idealized state, all objects fall with the same acceleration regardless of their mass. This remarkable fact, first demonstrated rigorously by Galileo Galilei and later explained by Newton's laws, seems counterintuitive because experience tells us feathers fall slower than rocks. The difference is due entirely to air resistance — in a vacuum, both hit the ground simultaneously.
On Earth's surface, the gravitational acceleration is g ≈ 9.8 m/s² (9.81 m/s² more precisely, varying slightly by latitude and altitude). This means a freely falling object gains approximately 9.8 m/s of speed every second. After 1 second it moves at 9.8 m/s, after 2 seconds at 19.6 m/s, and so on — until air resistance brings it to terminal velocity in real conditions.
The three key equations for free fall from rest are: v = gt (velocity after time t), d = ½gt² (distance fallen in time t), and v² = 2gd (velocity after falling distance d). If the object is thrown downward with initial velocity u, these become v = u + gt, d = ut + ½gt², and v² = u² + 2gd.
Free fall has profound applications beyond textbook physics: skydiving and parachute design, seismic measurement, spacecraft descent systems, construction safety calculations, and the measurement of g in different environments. On the Moon (g = 1.62 m/s²), free fall is 6× slower — the same object dropped from 5 m takes 2.5 seconds to reach the surface instead of 1.
Formula Reference Table
| Solve For | Formula (from rest) | Formula (initial velocity u) |
|---|---|---|
| Velocity (v) | v = g·t | v = u + g·t |
| Distance (d) | d = ½·g·t² | d = u·t + ½·g·t² |
| Time (t) | t = v/g = √(2d/g) | t = (v − u)/g |
| Velocity from height | v = √(2·g·d) | v² = u² + 2·g·d |
| g (Earth) | 9.8 m/s² | 32.2 ft/s² or 9.81 m/s² |
3 Worked Examples
A ball is dropped from a 44.1 m building. Find the time to hit the ground and impact velocity.
- Find time: t = √(2d/g) = √(2 × 44.1/9.8) = √9 = 3 seconds
- Find impact speed: v = g × t = 9.8 × 3 = 29.4 m/s
- Convert: 29.4 m/s = 105.8 km/h = 65.8 mph
Assuming free fall, how fast and how far does a skydiver fall in 12 seconds after jumping?
- Velocity: v = g × t = 9.8 × 12 = 117.6 m/s (423 km/h)
- Distance: d = ½ × 9.8 × 12² = ½ × 9.8 × 144 = 705.6 m
- In practice, terminal velocity (~53 m/s) is reached in ~10–14 s, so real distance is ~450 m
A hammer is dropped from 2 m height on Earth and on the Moon. Compare drop times.
- Earth (g = 9.8): t = √(2 × 2/9.8) = √0.408 = 0.639 s
- Moon (g = 1.62): t = √(2 × 2/1.62) = √2.47 = 1.57 s
- The Moon drop takes 2.46× longer — matching Apollo 15's famous hammer-feather demo
Real-World Applications
Common Mistakes to Avoid
The most common arithmetic error. Distance is NOT d = gt² — the ½ comes from integrating constant acceleration. A 5-second fall covers d = ½ × 9.8 × 25 = 122.5 m, not 245 m.
g is acceleration (m/s²), not force. The gravitational force on an object is F = mg (in newtons). You cannot plug weight (in kg-force) directly into free fall equations — convert to mass first.
If an object is thrown downward (not dropped from rest), the initial velocity u must be included: d = ut + ½gt², v = u + gt. Dropped from rest means u = 0 and the formulas simplify.
In air, objects reach terminal velocity (where drag = weight) and stop accelerating. Terminal velocity for a skydiver in spread-eagle position is ~53 m/s, far below what ideal free fall would predict after many seconds.
g varies by planet: Moon = 1.62, Mars = 3.72, Jupiter = 24.8 m/s². Problems set on other planets need the correct g. This calculator lets you set any g value using the custom input or planet presets.
If an object is thrown upward, it decelerates at g (opposing gravity). Set upward as positive: a = −g. The object rises until v = 0, then falls back. The free fall equations apply on the way down, with h = maximum height and u = 0 at the peak.
Frequently Asked Questions
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Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.