Free Fall Calculator
Our mechanics calculator computes fall accurately. Enter measurements for results with formulas and error analysis. See charts, tables, and visual results.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Free Fall Calculator
Calculator
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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 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.
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
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