Free Fall Calculator
Calculate free fall time, velocity, and distance using d = ½gt². Compare Earth, Moon, and Mars gravity. Includes fall time table from 1–10 seconds.
Free fall is motion under gravity alone, with no air resistance. The calculator gives you fall time, velocity at any point, and distance fallen — plus comparisons between Earth, Moon, and Mars.
Free Fall Formulas
Distance: d = ½ × g × t²
Velocity: v = g × t
Fall time: t = √(2d ÷ g)
Velocity from distance: v = √(2 × g × d)
Where:
- d = Distance fallen (metres)
- v = Velocity at time t (m/s)
- t = Time (seconds)
- g = Gravitational acceleration (9.81 m/s² on Earth)
Free Fall Table — Earth (g = 9.81 m/s²)
| Time (s) | Velocity (m/s) | Velocity (km/h) | Distance fallen (m) |
|---|---|---|---|
| 1 | 9.81 | 35.3 | 4.9 |
| 2 | 19.62 | 70.6 | 19.6 |
| 3 | 29.43 | 106.0 | 44.1 |
| 4 | 39.24 | 141.3 | 78.5 |
| 5 | 49.05 | 176.6 | 122.6 |
| 6 | 58.86 | 211.9 | 176.6 |
| 7 | 68.67 | 247.2 | 240.3 |
| 8 | 78.48 | 282.5 | 313.9 |
| 9 | 88.29 | 317.8 | 397.2 |
| 10 | 98.1 | 353.2 | 490.5 |
Note: In practice, air resistance limits velocity. A human body reaches terminal velocity of about 53–56 m/s (190–200 km/h) in a belly-to-earth position during skydiving, at around 12–15 seconds of free fall.
Common Fall Distances — How Long Do They Take?
| Drop height | Fall time | Impact velocity |
|---|---|---|
| 1 m (table height) | 0.45 s | 4.4 m/s (16 km/h) |
| 2 m (second floor balcony) | 0.64 s | 6.3 m/s (22.6 km/h) |
| 5 m (one storey) | 1.01 s | 9.9 m/s (35.6 km/h) |
| 10 m (three-storey building) | 1.43 s | 14 m/s (50.4 km/h) |
| 30 m (10-storey building) | 2.47 s | 24.3 m/s (87.5 km/h) |
| 100 m (Eiffel Tower base to first floor) | 4.51 s | 44.3 m/s (159 km/h) |
| 443 m (Empire State Building) | 9.5 s | 93.3 m/s (336 km/h)* |
*Without air resistance. Terminal velocity would be reached well before this in practice.
When Does the Free Fall Assumption Hold?
Free fall (no air resistance) is a useful approximation when:
- Heavy, compact objects falling short distances: A bowling ball dropped 5 metres — air resistance is negligible
- Introductory physics problems: Teachers specify "neglect air resistance" for this reason
- Vacuum conditions: The famous Apollo 15 demonstration on the Moon (hammer and feather falling identically)
Free fall is not accurate when:
- The object is light relative to its surface area (feather, sheet of paper, parachutist)
- The fall distance is long enough for air resistance to build up significantly
- The object has high drag (e.g., open parachute)
Gravity on Different Planets
| Location | g (m/s²) | Time to fall 10m | Impact speed |
|---|---|---|---|
| Earth | 9.81 | 1.43 s | 14.0 m/s |
| Moon | 1.62 | 3.51 s | 5.7 m/s |
| Mars | 3.72 | 2.32 s | 8.6 m/s |
| Venus | 8.87 | 1.50 s | 13.3 m/s |
| Jupiter (surface) | 24.79 | 0.90 s | 22.3 m/s |
| Sun (surface) | 274 | 0.27 s | 74.0 m/s |
On the Moon, you'd fall the same 10 metres but take 3.5 seconds instead of 1.43 — and hit at a little over a third of the Earth impact speed. This is why astronauts could jump higher on the Moon with the same leg force.
Terminal Velocity Explained
Terminal velocity is reached when air resistance exactly balances gravitational force — net force becomes zero and the object stops accelerating:
F_gravity = F_drag
mg = ½ × ρ × v² × C_d × A
Where ρ is air density, C_d is drag coefficient, and A is cross-sectional area.
| Object | Terminal velocity |
|---|---|
| Human (belly-down) | ~53–56 m/s (190–200 km/h) |
| Human (head-down) | ~90 m/s (320 km/h) |
| Cat | ~27 m/s (97 km/h) |
| Raindrop | 7–9 m/s (25–32 km/h) |
| Feather | ~0.5 m/s (1.8 km/h) |
| Skydiver with parachute | 5–6 m/s (18–22 km/h) |
Frequently Asked Questions
Do heavier objects fall faster than lighter ones?
In a vacuum, no — all objects fall at the same rate regardless of mass. Galileo demonstrated this (and legend has it he dropped balls from the Leaning Tower of Pisa). In air, heavier objects do fall faster if they have similar shapes and surface areas, because they have more gravitational force to overcome drag.
What is g exactly?
The standard gravitational acceleration used in physics is g = 9.80665 m/s² (exact, by definition). In practice, g varies slightly by location: it's about 9.78 m/s² at the equator (where Earth's rotation adds a centrifugal effect) and 9.83 m/s² at the poles. At altitude, g decreases with the inverse square of distance from Earth's centre.
How long does it take to fall 1,000 metres?
t = √(2 × 1,000 ÷ 9.81) = √203.9 = 14.3 seconds in a vacuum. In reality, a human body reaches terminal velocity in about 12–15 seconds and would take significantly longer — around 30–40 seconds — due to air resistance limiting acceleration after terminal velocity is reached.
What is the difference between free fall and terminal velocity?
In free fall (no air resistance or negligible air resistance), the object accelerates continuously at g m/s². At terminal velocity, air resistance equals gravitational force and the object moves at constant speed. Real falling objects start in a free-fall-like regime and asymptotically approach terminal velocity as speed increases.
Why does the formula use ½?
The ½ comes from integrating the constant acceleration over time: d = ∫v dt = ∫at dt = ½at². Starting from rest (v=0 at t=0), the average velocity during the fall is v_final ÷ 2 = gt ÷ 2, so distance = average velocity × time = (gt/2) × t = ½gt².
Related Calculators
- Velocity Calculator — speed, distance, and time from kinematics
- Force Calculator — calculate gravitational force F = mg
- Kinetic Energy Calculator — energy at impact from free fall
- Projectile Motion Calculator — add horizontal velocity to the fall