Free Fall Calculator
Calculate the time, velocity, and distance of an object in free fall using the equations h = ½gt², v = gt, and t = √(2h/g). Enter height or time along with gravitational acceleration to find all free fall parameters. See also our Projectile Motion Calculator and Kinetic Energy Calculator.
How to Calculate Free Fall
Free fall is the motion of an object under the sole influence of gravity, with no air resistance or other forces acting upon it. This idealized motion was first studied systematically by Galileo Galilei in the late 16th century, who demonstrated that all objects fall at the same rate regardless of their mass — a revolutionary insight that contradicted Aristotle's teachings that had dominated for nearly two millennia.
To calculate free fall parameters, you need to understand three fundamental equations of motion under constant acceleration. When an object is dropped from rest (initial velocity = 0), the distance fallen equals one-half times gravity times time squared (h = ½gt²). The velocity at any point during the fall equals gravity times time (v = gt). And the time to fall a given height equals the square root of two times height divided by gravity (t = √(2h/g)).
These equations assume constant gravitational acceleration, which is approximately 9.81 m/s² at Earth's surface. In reality, gravity varies slightly with altitude and latitude — from about 9.78 m/s² at the equator to 9.83 m/s² at the poles. For most practical calculations near Earth's surface, 9.81 m/s² provides excellent accuracy. On other celestial bodies, gravity differs significantly: the Moon has 1.62 m/s², Mars has 3.72 m/s², and Jupiter has 24.79 m/s².
The key insight of free fall physics is that acceleration is constant. This means velocity increases linearly with time, while distance increases quadratically. An object that has fallen for 2 seconds has traveled 4 times farther than one that has fallen for 1 second. This quadratic relationship explains why falling from greater heights is disproportionately more dangerous — the impact velocity grows with the square root of height.
Free Fall Formulas
Distance fallen (from rest):
h = ½gt²
Final velocity (from rest):
v = gt
Time to fall height h:
t = √(2h/g)
Velocity after falling height h:
v = √(2gh)
With initial velocity v₀ (downward positive):
h = v₀t + ½gt²
v = v₀ + gt
v² = v₀² + 2gh
Standard gravity values:
Earth: g = 9.81 m/s² | Moon: 1.62 m/s²
Mars: 3.72 m/s² | Jupiter: 24.79 m/s²
Example Calculation
An object is dropped from a height of 100 meters on Earth. Calculate the time to hit the ground and the impact velocity:
Given: h = 100 m, g = 9.81 m/s², v₀ = 0
Time: t = √(2h/g) = √(2×100/9.81) = √(20.387) = 4.515 s
Final velocity: v = gt = 9.81 × 4.515 = 44.29 m/s
Or: v = √(2gh) = √(2×9.81×100) = √(1962) = 44.29 m/s ✓
Convert to km/h: 44.29 × 3.6 = 159.4 km/h
Average velocity: v_avg = v/2 = 22.15 m/s
Verify: h = v_avg × t = 22.15 × 4.515 ≈ 100 m ✓
Free Fall Reference Table
| Height (m) | Time (s) | Impact Velocity (m/s) |
|---|---|---|
| 1 m | 0.452 s | 4.43 m/s |
| 5 m | 1.010 s | 9.90 m/s |
| 10 m | 1.428 s | 14.01 m/s |
| 20 m | 2.019 s | 19.81 m/s |
| 50 m | 3.193 s | 31.32 m/s |
| 100 m | 4.515 s | 44.29 m/s |
| 200 m | 6.386 s | 62.64 m/s |
| 500 m | 10.096 s | 99.05 m/s |
| 1000 m | 14.278 s | 140.07 m/s |
| 5000 m | 31.928 s | 313.21 m/s |
Frequently Asked Questions
What is free fall in physics?
Free fall is the motion of an object where gravity is the only force acting upon it. In true free fall, there is no air resistance, thrust, or any other force — only gravitational acceleration. On Earth, this means the object accelerates downward at approximately 9.81 m/s². Astronauts in orbit experience continuous free fall (they are falling around the Earth), which is why they appear weightless. A skydiver before opening their parachute approximates free fall, though air resistance does play a role at higher speeds.
Do heavier objects fall faster?
No. In a vacuum (true free fall), all objects fall at exactly the same rate regardless of mass. This was demonstrated by Galileo and later confirmed dramatically on the Moon by Apollo 15 astronaut David Scott, who dropped a hammer and feather simultaneously — both hit the ground at the same time. In air, heavier objects may appear to fall faster because air resistance has less relative effect on them, but the gravitational acceleration is identical for all masses.
What is terminal velocity?
Terminal velocity is the maximum speed an object reaches when falling through a fluid (like air) when the drag force equals the gravitational force. At terminal velocity, acceleration becomes zero and the object falls at constant speed. For a human skydiver in a spread-eagle position, terminal velocity is about 55 m/s (200 km/h). In a head-down position, it can reach 90 m/s (320 km/h). Terminal velocity depends on mass, cross-sectional area, drag coefficient, and air density.
How does air resistance affect free fall?
Air resistance (drag) opposes motion and increases with velocity. For low speeds, drag is proportional to velocity; at higher speeds, it's proportional to velocity squared. This means the free fall equations (h = ½gt²) are only accurate for short falls or dense objects. For a baseball dropped from 100 m, air resistance reduces the impact speed by about 10%. For a feather, air resistance dominates almost immediately, making the free fall equations essentially inapplicable.
How do you calculate free fall on other planets?
The same formulas apply — just substitute the appropriate gravitational acceleration. On the Moon (g = 1.62 m/s²), objects fall about 6 times slower than on Earth. On Mars (g = 3.72 m/s²), they fall about 2.6 times slower. On Jupiter (g = 24.79 m/s²), they fall about 2.5 times faster. For example, dropping an object from 10 m: on Earth it takes 1.43 s, on the Moon 3.51 s, on Mars 2.32 s, and on Jupiter 0.90 s.
What is the difference between free fall and projectile motion?
Free fall is purely vertical motion under gravity (no horizontal component). Projectile motion includes both horizontal and vertical components — the object moves forward while falling. In projectile motion, the vertical component is identical to free fall (accelerating at g downward), while the horizontal component remains constant (no horizontal acceleration in ideal conditions). A ball dropped from a cliff undergoes free fall; a ball thrown horizontally from the same cliff undergoes projectile motion, hitting the ground at the same time but farther away.
Applications of Free Fall Physics
Free fall physics has numerous practical applications. Engineers use these equations to design safety systems like airbags and crumple zones, calculating impact forces from fall heights. Architects consider free fall when designing buildings and safety barriers. Sports scientists analyze the trajectories of balls and athletes. Geophysicists use precise free fall measurements to map underground density variations for mineral exploration. Even amusement park designers use free fall equations to create thrilling yet safe drop rides.
In space exploration, free fall is fundamental. Spacecraft in orbit are in continuous free fall around Earth, creating microgravity conditions used for scientific research. The International Space Station falls toward Earth at the same rate it moves forward, creating a stable orbit. Understanding free fall on other planets is essential for landing spacecraft — Mars landers must account for Mars's lower gravity when calculating descent trajectories and parachute deployment timing.