Free Fall Calculator
Calculate free fall time, impact velocity, distance fallen, and impact energy. Supports custom gravity for any planet. Enter height, time, or velocity.
Free Fall Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser — no data is sent to any server.
Formula: h = ½gt² | v = gt | v² = 2gh | KE = ½mv²
Worked example — t = 3.19s | v = 31.3 m/s (112.8 km/h) | KE = 245.2J
Formula
h = ½gt² | v = gt | v² = 2gh | KE = ½mv²
Free fall kinematics: distance fallen equals half of gravitational acceleration times time squared. Velocity equals g times time. These equations assume no air resistance and constant gravitational acceleration. Impact kinetic energy equals half mass times velocity squared.
Worked Examples
Example 1: Dropped Object from Building
Problem:A ball is dropped from the top of a 50m building on Earth. How long does it take to hit the ground, and what is the impact velocity? The ball has mass 0.5 kg.
Solution:h = 50m, v₀ = 0, g = 9.81 m/s² Fall time: t = √(2h/g) = √(100/9.81) = 3.193 s Impact velocity: v = gt = 9.81 × 3.193 = 31.32 m/s Converted: 31.32 × 3.6 = 112.8 km/h Kinetic energy: KE = ½mv² = 0.5 × 0.5 × 31.32² = 245.2 J Potential energy: PE = mgh = 0.5 × 9.81 × 50 = 245.3 J ✓
Result:t = 3.19s | v = 31.3 m/s (112.8 km/h) | KE = 245.2J
Example 2: Free Fall on Mars
Problem:How far does an object fall in 5 seconds on Mars (g = 3.72 m/s²) if thrown downward at 2 m/s?
Solution:t = 5s, v₀ = 2 m/s, g = 3.72 m/s² Distance: d = v₀t + ½gt² = 2×5 + 0.5×3.72×25 = 10 + 46.5 = 56.5m Final velocity: v = v₀ + gt = 2 + 3.72×5 = 20.6 m/s Converted: 20.6 × 3.6 = 74.2 km/h
Result:d = 56.5m | v = 20.6 m/s (74.2 km/h)
Frequently Asked Questions
What is free fall?
Free fall is the motion of an object falling under the sole influence of gravity, with no air resistance or other forces acting on it. In free fall, all objects accelerate at the same rate regardless of mass — this was famously demonstrated by Galileo and later confirmed by Apollo 15 astronauts dropping a hammer and feather on the Moon. On Earth, free fall acceleration (g) is approximately 9.81 m/s² (32.2 ft/s²). The basic kinematic equations are: distance = ½gt², velocity = gt, and v² = 2gh (for objects starting from rest). Free fall is an idealization; real falling objects experience air resistance.
How do you calculate fall time from height?
For an object dropped from rest (v₀ = 0) from height h: Time = √(2h/g). For example, dropping from 100m on Earth: t = √(2×100/9.81) = √20.39 = 4.52 seconds. With an initial downward velocity v₀: use the quadratic formula on h = v₀t + ½gt², giving t = [-v₀ + √(v₀² + 2gh)] / g. Common fall times on Earth: 1 second = 4.9m, 2 seconds = 19.6m, 3 seconds = 44.1m, 5 seconds = 122.6m, 10 seconds = 490.5m.
What is impact velocity?
Impact velocity is the speed of an object at the moment it strikes the ground (or another surface). For free fall from rest: v = √(2gh), where g is gravitational acceleration and h is the fall height. For example, falling 10m on Earth: v = √(2×9.81×10) = 14.0 m/s = 50.4 km/h. Impact velocity can also be calculated from fall time: v = gt (from rest) or v = v₀ + gt (with initial velocity). In practice, air resistance limits the maximum speed to the terminal velocity, which depends on the object's mass, shape, and cross-sectional area.
What is the difference between free fall and terminal velocity?
Free fall assumes no air resistance — the object continuously accelerates at g. In reality, air resistance (drag) increases with speed. Terminal velocity is reached when drag force equals gravitational force, so acceleration becomes zero and speed remains constant. Terminal velocities vary greatly: skydiver (belly-down) ≈ 53 m/s (190 km/h), skydiver (head-down) ≈ 90 m/s (320 km/h), baseball ≈ 42 m/s (150 km/h), tennis ball ≈ 31 m/s (110 km/h), raindrop ≈ 9 m/s (32 km/h). Free fall calculations are accurate for short falls, dense objects, or vacuum conditions.
How does gravity differ on other planets?
Gravitational acceleration varies by celestial body based on mass and radius: Earth = 9.81 m/s², Moon = 1.62 m/s² (16.5% of Earth), Mars = 3.72 m/s² (37.9%), Venus = 8.87 m/s² (90.4%), Jupiter = 24.79 m/s² (252.7%), Saturn = 10.44 m/s² (106.4%), Mercury = 3.70 m/s² (37.7%), Sun = 274 m/s² (2,793%). An object dropped from 100m takes 4.52s on Earth, 11.11s on the Moon, and 2.84s on Jupiter. Your weight on the Moon is about 1/6 of Earth, and on Jupiter about 2.5x Earth.
Why doesn't mass affect how fast an object falls?
Gravity pulls with a force proportional to mass, F = mg, but acceleration is force divided by mass, so a = mg/m = g and the mass cancels exactly. A 1 kg and a 100 kg sphere released together reach the ground at the same instant in a vacuum. Mass only re-enters the problem through air resistance, because drag depends on size and shape rather than mass, which is why a feather and a hammer separate in air but not on the Moon.
How do the free fall equations handle an object thrown upward?
Treat upward velocity as negative when down is positive, and the same equations cover the whole flight. The object rises for t = v₀/g and reaches a maximum height of v₀²/(2g) above the launch point. Thrown up at 20 m/s on Earth it climbs for 20/9.81 = 2.04 s to 400/19.62 = 20.4 m, then falls back through the launch height at the same 20 m/s. Ascent and descent are mirror images when drag is ignored.
Why does a falling object cover a greater distance during each successive second?
Distance grows with t², so the increments follow the odd numbers 1 : 3 : 5. Starting from rest on Earth, the first second covers ½ × 9.81 × 1 = 4.90 m, the second second adds 14.72 m and the third adds 24.53 m, for 44.15 m in total after three seconds. The object is faster throughout each later interval, which is why fall height climbs so steeply while fall time changes comparatively little.
Why is g not exactly 9.81 m/s² everywhere on Earth?
Earth is an oblate spheroid that also spins, so surface gravity ranges from about 9.78 m/s² at the equator, where the radius is largest and centrifugal effect greatest, to about 9.83 m/s² near the poles; 9.80665 m/s² is the agreed standard value. Altitude matters too, since g falls off as 1/r²: at 10 km the value drops roughly 0.3 percent. For everyday drops these differences shift the answer by well under one percent.
Why are astronauts weightless if they are still in Earth's gravity?
They are in continuous free fall. At the International Space Station's altitude g is still around 8.7 m/s², roughly 89 percent of its surface value, but the station and everything in it accelerate toward Earth together while moving sideways fast enough that the curved path never intersects the ground. With no support force pressing back, nothing has apparent weight. The same sensation occurs briefly in a dropped lift or on a parabolic aircraft flight.
References
Background & Theory
Free Fall Time Across the Solar System
Because free fall assumes no air resistance, the only variable that changes between locations is gravitational acceleration g, which depends on a planet's mass and radius. Comparing fall times for the same drop height makes the differences concrete.
| Body | Gravity (m/s^2) | Time to fall 100m |
|---|---|---|
| Moon | 1.62 | ~11.11 s |
| Mars | 3.72 | ~7.33 s |
| Earth | 9.81 | ~4.52 s |
| Jupiter (cloud-top gravity) | 24.79 | ~2.84 s |
Apollo 15 astronaut David Scott famously dropped a hammer and a feather on the airless Moon in 1971, and both hit the ground at the same instant — direct proof that, absent air resistance, gravitational acceleration is independent of an object's mass, exactly as this calculator assumes.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
Related Calculators
🧮Acceleration Calculator
Calculate acceleration with inputs, formulas, and instant results.
🧮Motion on Incline with Friction Calculator
Calculate motion on incline with friction with inputs, formulas, and instant results.
🧮Relative Velocity Calculator
Calculate relative velocity with inputs, formulas, and instant results.
🧮Velocity Calculator
Calculate velocity with inputs, formulas, and instant results.
🧮Coupled Spring Damper Calculator
Calculate coupled spring damper with inputs, formulas, and instant results.
🧮Friction Force Calculator
Calculate friction force with inputs, formulas, and instant results.
🧮Impulse Calculator
Calculate impulse with inputs, formulas, and instant results.
🧮Variable Mass System Calculator
Calculate variable mass system with inputs, formulas, and instant results.