Free Fall Calculator

General Physics

This tool calculates the time and final velocity of an object in free fall, considering its initial velocity and the gravitational pull.

Practical Examples

See how the Free Fall Calculator works with these real-world scenarios.

Dropping a Ball from a Tower

Example 1

A ball is dropped from a 150-meter-tall tower with no initial velocity. Calculate its time of fall and impact velocity on Earth.

H: 150 m, V₀: 0 m/s, g: 9.81 m/s²

Object Thrown Downwards

Example 2

An object is thrown downwards from a cliff 80 meters high with an initial velocity of 10 m/s. Find its fall time and final speed.

H: 80 m, V₀: 10 m/s, g: 9.81 m/s²

Free Fall on the Moon

Example 3

An astronaut drops a rock from a height of 50 meters on the Moon. How long does it take to hit the ground and at what speed?

H: 50 m, V₀: 0 m/s, g: 1.62 m/s²

Skydiver in Early Stage of Fall

Example 4

Assuming no air resistance, calculate the speed of a skydiver after falling for 400 meters, having started from rest.

H: 400 m, V₀: 0 m/s, g: 9.81 m/s²

Other Titles
Understanding the Free Fall Calculator: A Comprehensive Guide
Dive deep into the physics of free fall, from basic concepts to complex calculations and real-world applications.

What is Free Fall?

  • Defining Free Fall
  • The Role of Gravity
  • Ideal vs. Real-World Conditions
Free fall is the motion of a body where gravity is the only force acting upon it. In a true free fall, factors like air resistance are considered negligible. This idealized state is what our calculator models to provide accurate results based on kinematic equations.
The Constant Pull of Gravity
The acceleration due to gravity (g) is the constant rate at which objects accelerate towards the Earth (or another celestial body). On Earth, this value is approximately 9.81 m/s². This means that for every second an object is in free fall, its downward velocity increases by 9.81 meters per second. Our calculator uses this value by default but allows you to adjust it for calculations on other planets or in different scenarios.
Air Resistance and Terminal Velocity
In reality, a falling object experiences air resistance, a frictional force that opposes its motion. As the object's speed increases, so does air resistance, until it balances the force of gravity. At this point, the object stops accelerating and reaches a constant speed known as terminal velocity. This calculator operates under the assumption of ideal conditions, meaning air resistance is ignored.

Step-by-Step Guide to Using the Free Fall Calculator

  • Inputting Your Data
  • Interpreting the Results
  • Using the Reset and Example Features
Our calculator is designed for ease of use. Follow these simple steps to get your results:
1. Enter the Height
In the 'Height / Distance (m)' field, input the vertical distance from which the object will fall. This value must be in meters.
2. Provide Initial Velocity
In the 'Initial Velocity (m/s)' field, enter the object's starting speed. If the object is simply dropped, the initial velocity is 0. If it's thrown downwards, enter a positive value. Note: This calculator does not model objects thrown upwards.
3. Set the Gravity
The 'Gravity (m/s²)' field is pre-filled with Earth's standard gravity (9.81 m/s²). You can change this value to calculate free fall on other celestial bodies like the Moon (1.62 m/s²) or Mars (3.72 m/s²).
4. Calculate and Analyze
Click the 'Calculate' button. The calculator will instantly display the 'Time of Fall' in seconds and the 'Final (Impact) Velocity' in m/s.

Mathematical Derivation and Formulas

  • The Core Kinematic Equations
  • Deriving Time of Fall
  • Deriving Final Velocity
The calculations are based on the fundamental kinematic equations for uniformly accelerated motion. The primary equations are:
d = v₀t + (1/2)gt²
v = v₀ + gt
v² = v₀² + 2gd
Calculating Final Velocity (v)
The final velocity is calculated using the formula v = sqrt(v₀² + 2gd), where 'v₀' is the initial velocity, 'g' is gravity, and 'd' is the height. This equation directly relates the final speed to the initial speed and the distance fallen.
Calculating Time of Fall (t)
Once the final velocity (v) is known, the time of fall can be found by rearranging the formula v = v₀ + gt. The resulting formula is t = (v - v₀) / g. This gives the total duration the object is in the air.

Calculation Example

  • Given: Height (d) = 100 m, Initial Velocity (v₀) = 0 m/s, Gravity (g) = 9.81 m/s².
  • 1. Final Velocity (v) = sqrt(0² + 2 * 9.81 * 100) = sqrt(1962) ≈ 44.29 m/s.
  • 2. Time (t) = (44.29 - 0) / 9.81 ≈ 4.52 seconds.

Real-World Applications of Free Fall

  • Physics and Engineering
  • Amusement Park Rides
  • Space Exploration
The principles of free fall are fundamental in many scientific and engineering fields.
Civil Engineering and Safety
Engineers use free fall calculations to design structures and ensure safety. For example, understanding the impact force of a dropped object is crucial for designing protective barriers and safety nets on construction sites.
Designing Thrills
The exhilarating feeling on a drop tower ride at an amusement park is a direct application of free fall. Ride designers use these principles to control the drop speed and ensure the ride is both thrilling and safe.
Planetary Science
Scientists use free fall data to study the gravitational fields of other planets and moons. By dropping probes and analyzing their descent, they can determine the mass and composition of celestial bodies.

Common Misconceptions

  • Heavier Objects Fall Faster
  • Acceleration Changes During Fall
  • The 'Weightless' Illusion
The Myth of Mass and Speed
A famous misconception, disproven by Galileo, is that heavier objects fall faster than lighter ones. In a vacuum, all objects fall at the same rate of acceleration regardless of their mass. Air resistance is what can make a feather fall slower than a bowling ball in the real world, not its mass.
Constant Acceleration
Another common error is believing that an object's acceleration changes as it falls. In an ideal free fall, the acceleration 'g' is constant throughout the motion. The velocity changes, but the rate of that change (acceleration) does not.
Astronauts and 'Zero Gravity'
Astronauts in orbit appear weightless, which is often described as being in 'zero gravity.' In reality, they are in a continuous state of free fall. The International Space Station and everything in it are constantly falling towards Earth, but they have enough horizontal velocity to continuously 'miss' it, resulting in an orbit. The feeling of weightlessness is the sensation of constant fall.