Article — Free Fall Calculator
Free Fall: Equations, Physics, and Records
Free fall is motion under gravity alone, starting from rest. On Earth, an object falls a distance h = ½gt² in time t, reaching velocity v = gt at impact. With g = 9.81 m/s², a 5-meter drop takes 1.01 seconds and lands at 9.9 m/s (35 km/h). The equations are exact in vacuum but underestimate fall times in air because of drag.
Free fall is the simplest case of accelerated motion — one variable, one constant. It is also a foundational topic in physics education, because it lets students touch the concept of constant acceleration without the complications of friction, drag, or curved paths. Galileo, Newton, Einstein, and every undergraduate physics class since 1600 has worked through these same equations.
What is free fall?
Free fall is the motion of an object under the influence of gravity alone, with no other forces acting on it. The object starts from rest and accelerates downward at the local gravitational acceleration g. On Earth's surface, g = 9.80665 m/s² by definition (slightly varying with latitude and altitude in practice). On the Moon, g = 1.62 m/s². In deep space far from any large mass, g ≈ 0.
The technical definition excludes air resistance. Real falls in atmosphere experience drag, which limits velocity and eventually balances gravity at the terminal velocity. For short falls (a few meters) drag is negligible and the textbook equations work. For long falls (hundreds of meters), drag dominates and the actual fall takes much longer than the vacuum formulas predict.
Astronauts aboard the International Space Station are in continuous free fall — they fall "around" the Earth, never hitting it because they have enough horizontal velocity to keep missing. The weightless feeling is not the absence of gravity (which is still 90% of surface value at that altitude) but the absence of contact forces. They are falling alongside the station.
The free-fall equations
Four equations cover every free-fall problem. Pick whichever pair matches your known and unknown:
h = ½gt² v = gtt = √(2h/g) v = √(2gh)g = 9.81 m/s² (Earth) g = 32.2 ft/s² (US units)These come from integrating the constant-acceleration definition: a = dv/dt = g (constant), v = ∫g dt = gt, h = ∫v dt = ½gt². The √ form pops out when you solve for time or velocity given the distance.
A useful intuition: after one second on Earth, an object has fallen 4.9 m and moves at 9.8 m/s. After two seconds, 19.6 m and 19.6 m/s. After three seconds, 44.1 m and 29.4 m/s. The distance grows quadratically; the velocity grows linearly. Doubling the fall time gives four times the distance, twice the velocity.
Free fall on other planets
The equations don't change between planets — only g does. Mars at 3.72 m/s² gives much slower falls than Earth; Jupiter at 24.79 m/s² makes things crash down 2.5× faster. The Moon at 1.62 m/s² is famously gentle, which is why Apollo astronauts could afford to bounce as they walked.
Jupiter and Saturn don't actually have solid surfaces, so "dropping" something there means falling into a thickening atmosphere of hydrogen and helium that crushes objects long before they reach any solid core. The g values still tell you the gravitational pull at the cloud tops, useful for comparing the gas giants to terrestrial planets.
Free fall vs terminal velocity
Real falls in Earth's atmosphere don't follow v = gt for long. Air drag grows with velocity squared, eventually matching gravity. At that balance point, called terminal velocity, the object continues at constant speed rather than accelerating further.
For a human in skydiving belly-down position, terminal velocity is about 55 m/s (200 km/h) — reached after roughly 12 seconds of fall. Falls shorter than 200 m are well approximated by free-fall equations; longer falls require drag-aware physics.
- Raindrop (3 mm) = 9 m/s (32 km/h)
- Tennis ball = 50 m/s (180 km/h)
- Person (belly-down) = 55 m/s (198 km/h)
- Person (head-first) = 90 m/s (324 km/h)
- Skydiver with open chute = 5–6 m/s (18–22 km/h)
- Apollo lunar feather = no terminal (no air)
Terminal velocity depends on mass, cross-sectional area, drag coefficient, and air density. Skydivers control descent speed by changing body posture (frontal area). Parachutes work by drastically raising the drag coefficient, dropping terminal velocity to safely survivable speeds.
Famous free-fall experiments
Free fall has been the subject of some of the most famous experiments in the history of physics:
- Galileo's inclined plane (~1604). Galileo couldn't time freely falling objects accurately, so he rolled balls down inclined planes (which slow the fall to manageable speeds). He showed the distance covered grew with the square of the time — establishing the t² relationship that bears his name.
- Newton's apple (legend, 1665). Whether or not the apple really fell on Newton's head, the story captures the moment he realized that the same gravity pulling an apple down also keeps the Moon in orbit. His Principia (1687) formalized universal gravitation and made free-fall a special case of orbital motion.
- Apollo 15 hammer-feather drop (1971). Astronaut David Scott dropped a 1.32 kg geological hammer and a 30 g falcon feather simultaneously on the lunar surface. Both hit the ground at the same instant — vindicating Galileo three centuries later, in front of a live TV audience.
- Einstein's elevator (1907). Einstein proposed that an observer in free fall feels no gravity — the equivalence principle. This thought experiment led to general relativity and the modern understanding of gravity as the curvature of spacetime.
Free-fall skydiving records
Modern skydivers have pushed free fall to extraordinary heights and speeds. Three benchmark records:
- Joe Kittinger (1960) = 31.3 km from a balloon — held record for 52 years
- Felix Baumgartner (2012) = 38.97 km, peak 1341 km/h (Mach 1.25)
- Alan Eustace (2014) = 41.42 km, current record holder
- Free-fall time (Eustace) ≈ 4 min 27 s (15 min total descent including parachute)
- Max altitude in stratosphere = thin air allows extreme speeds
All three exceeded supersonic speed during the fall, breaking the sound barrier with their bodies. At those altitudes the atmosphere is so thin that drag is minimal — they accelerate close to vacuum free-fall predictions until denser air decelerates them.
Free-fall rules of thumb
Quick mental approximations for Earth-surface free fall (using g ≈ 10 m/s² instead of 9.81 introduces about 2% error — fine for estimates):
- Distance ≈ 5t² in meters, where t is seconds. 1 s → 5 m; 2 s → 20 m; 3 s → 45 m; 5 s → 125 m.
- Velocity ≈ 10t in m/s, or ≈ 35t in km/h. After 3 s: 30 m/s (108 km/h).
- Average velocity ≈ 5t m/s, half the impact velocity for a fall from rest.
- Time for short drops: square root of (height in m / 5). 20 m drop ≈ √4 = 2 s.
Free-fall calculation pitfalls
A skydiver from 4000 m doesn't fall for √(2 × 4000 / 9.81) = 28.6 s. Terminal velocity caps acceleration after about 12 seconds; the rest of the descent is at constant ~55 m/s. The actual free-fall portion takes about 75–80 seconds. Use vacuum equations only for short falls.
Other common errors:
- Forgetting the ½. h = gt² (without the ½) gives twice the correct distance. A widespread typo in physics homework.
- Mixing units. Using g = 32.2 ft/s² with h in meters gives nonsense. Pick a unit system and stay in it.
- Assuming initial velocity is zero. Free-fall starts from rest. If the object is thrown downward, add v₀t to the height equation: h = v₀t + ½gt².
- Ignoring air resistance for long falls. Anything over 200 m on Earth needs drag-aware physics.
- Using sea-level g everywhere. The 0.5% variation between equator and pole is usually negligible, but the 1% drop at typical airliner altitude can matter for atmospheric science.
- Confusing free-fall with weightless flight. A "vomit comet" aircraft creates ~25 seconds of free-fall conditions for astronaut training — passengers feel weightless, but they're falling along with the aircraft, not floating.