Physics calculators

Free Fall Calculator

Updated Aug 2, 2026 By Jehan Wadia
4.4 · Rate Formulas
What do you want to solve for?
Enter the drop height and the initial velocity. The calculator will return the time of fall.
Motion Type & Unit System
Sign convention: downward is positive.
Switches every unit menu and converts the values you already entered.
Inputs
Distance from release point to the finish point.
Always a positive magnitude — direction is set above.
Time elapsed from release to the finish point.
Positive = moving downward at the end of the fall.
Air Resistance
The proportionality constant in the drag force F = k·v.
Terminal velocity and drag effects are computed using a linear drag model (F = k·v).

Fall Time (t)
 
Final Velocity (v)
 
Drop Height (h)
 
Initial Velocity (v₀)
 
 
Average Speed
 
Gravity Used (g)
 
Step-by-Step Solution
Distance & Velocity vs. Time
Motion Table
TimeDistance fallenVelocity

Introduction

Free fall happens when an object drops under the pull of gravity alone, with no other forces acting on it. Whether you're solving a physics homework problem or just curious how long it takes a ball to hit the ground, our Free Fall Calculator gives you quick and accurate answers. Enter a height, pick a planet, and instantly find the fall time, final velocity, kinetic energy, and more — all with step-by-step solutions and clear graphs.

This tool covers four key modes: simple free fall from rest, free fall with an initial velocity (like throwing a ball upward), an energy calculator that shows potential and kinetic energy, and an advanced mode that factors in air resistance and terminal velocity. You can switch between units such as meters, feet, kilometers, and miles, and even compare how gravity works on Earth, the Moon, Mars, Jupiter, and other celestial bodies. Each calculation displays the formulas used and walks you through every step so you can learn the physics behind the numbers.

How to use our Free Fall Calculator

Pick what you want to find, enter the values you already know, and the calculator gives you the fall time, final speed, drop height, or starting speed, plus a step-by-step solution, a chart, and a motion table.

What do you want to solve for: Choose Fall Time, Final Velocity, Drop Height, or Initial Velocity. This is the answer the calculator will find.

Known values: Pick the pair of values you already have, like height and starting speed. Only the boxes you need will show up.

Motion Type: Choose if the object was dropped from rest, thrown down, or thrown up. Down counts as positive.

Unit System Preset: Click Metric or Imperial. All unit menus switch, and any numbers you typed are converted for you.

Gravity: Pick a planet or the Moon, or choose Custom and type your own value in m/s², ft/s², or g.

Drop Height (h): Type how far the object falls, then pick the unit (m, ft, km, mi, and more).

Initial Velocity (v₀): Type the speed at the moment of release as a positive number. The Motion Type sets the direction.

Fall Time (t): Type how long the fall lasts and pick seconds, milliseconds, minutes, or hours. It must be more than zero.

Final / Impact Velocity (v): Type the speed at the end of the fall and choose the unit. A positive number means it is moving down.

Include Air Resistance: Turn this switch on to use a linear drag model. It also shows terminal velocity and impact energy.

Mass (m): With air resistance on, type the object's mass in kg, g, lb, or oz.

Drag Constant (k): With air resistance on, type the drag constant from F = k·v in kg/s or lb/s.

Calculate and Reset: Click Calculate to see your results, or Reset to go back to the starting values. You can also change the output units on each result card.

Understanding Free Fall

Free fall is the motion of an object falling only under the influence of gravity, with no other forces acting on it. When you drop a ball, jump off a diving board, or watch a raindrop fall from the sky, you are seeing free fall in action. During free fall, every object speeds up at the same steady rate regardless of its mass. On Earth, that rate is about 9.8 meters per second squared (9.8 m/s²), which means an object's speed increases by roughly 9.8 m/s for every second it falls. This constant increase in speed is a form of acceleration, which you can explore further with our Acceleration Calculator.

Key Free Fall Formulas

Three main equations describe free fall when an object starts from rest:

  • Time to fall: t = √(2h / g) — This tells you how long it takes an object to hit the ground when dropped from height h.
  • Final velocity: v = g × t — This gives the speed of the object right before it hits the ground.
  • Distance fallen: d = ½ × g × t² — This tells you how far the object has fallen after a certain amount of time. You can use our Displacement Calculator to work with more complex distance and displacement problems.

In these formulas, g stands for gravitational acceleration, t is time, h is height, and v is velocity. These equations assume there is no air resistance slowing the object down.

Free Fall with Initial Velocity

Sometimes an object isn't simply dropped — it's thrown upward or downward. When you throw a ball straight up, it slows down, stops for an instant at its highest point, and then falls back down. The full equation for height at any time is y = y₀ + v₀t − ½gt², where v₀ is the starting velocity (positive if thrown upward, negative if thrown downward) and y₀ is the starting height. The object reaches its maximum height when all upward velocity is used up, which happens at time t = v₀ / g. If the object is launched at an angle rather than straight up or down, you'll want to use our Projectile Motion Calculator instead.

Energy in Free Fall

Energy is always conserved during free fall. At the top, an object has potential energy (PE = mgh), which is stored energy due to its height. You can calculate this precisely with our Potential Energy Calculator. As it falls, that potential energy turns into kinetic energy (KE = ½mv²), which is the energy of motion — use our Kinetic Energy Calculator to explore this in more detail. Right before hitting the ground, nearly all the potential energy has become kinetic energy. The total mechanical energy — potential plus kinetic — stays the same throughout the fall, as long as air resistance is ignored.

The Role of Air Resistance

In real life, air pushes back against a falling object. This push is called air resistance or drag. As an object falls faster, the drag force grows until it equals the pull of gravity. At that point, the object stops speeding up and falls at a constant speed called terminal velocity. Terminal velocity depends on the object's mass, shape, size, and the density of the air. A skydiver in a spread-eagle position has a terminal velocity of about 55 m/s (roughly 120 mph), while a streamlined object like a bullet falls much faster. Understanding the balance between gravitational force and drag force is key — our Force Calculator can help you analyze forces in different scenarios.

Gravity on Other Planets

Gravity is not the same everywhere. On the Moon, gravitational acceleration is only about 1.6 m/s², so objects fall much slower and you could jump much higher. On Jupiter, gravity is a powerful 24.8 m/s², meaning objects fall about 2.5 times faster than on Earth. This is why the calculator lets you pick different celestial bodies — the same drop height produces very different fall times and impact speeds depending on where you are in the solar system. For an extreme example of gravity, our Schwarzschild Radius Calculator lets you explore the gravitational boundaries of black holes.

Real-World Examples of Free Fall

Free fall physics shows up in many everyday and extreme situations. A penny dropped from the Empire State Building (443 meters) takes about 9.5 seconds to reach the ground and hits at roughly 93 m/s without air resistance. In 2012, Felix Baumgartner jumped from 39,045 meters above Earth and reached speeds over 370 m/s before air resistance slowed him down. Galileo's famous experiment at the Leaning Tower of Pisa demonstrated that two objects of different mass hit the ground at the same time when dropped from the same height, proving that gravity accelerates all objects equally. When a falling object strikes the ground, the rapid change in velocity creates a large force — you can analyze this using our Impulse Calculator or Momentum Calculator to understand the impact dynamics.


Formulas used

Displacement (no drag)
h = v_0 t + \tfrac{1}{2} g t^2
Fall time from height and initial velocity
t = \frac{-v_0 + \sqrt{v_0^2 + 2gh}}{g}
Final velocity from time
v = v_0 + g t
Time-independent velocity relation
v^2 = v_0^2 + 2gh
Terminal velocity and time constant (linear drag)
v_t = \frac{mg}{k}, \qquad \tau = \frac{m}{k}
Velocity with linear drag
v(t) = v_t + (v_0 - v_t)e^{-t/\tau}
Distance fallen with linear drag
h(t) = v_t t + (v_0 - v_t)\tau\left(1 - e^{-t/\tau}\right)
Average speed and impact kinetic energy
\bar v = \frac{h}{t}, \qquad KE = \tfrac{1}{2} m v^2

Frequently asked questions

What is free fall in physics?

Free fall is when an object falls only because of gravity, with no other forces pushing or pulling it. There is no motor, no parachute, and no thrust — just gravity pulling the object down. In free fall, all objects speed up at the same rate no matter how heavy they are.

Does mass affect how fast an object falls in free fall?

No. In true free fall (with no air resistance), all objects fall at the same rate regardless of their mass. A bowling ball and a feather dropped in a vacuum hit the ground at the same time. Mass only matters when air resistance is involved, because heavier objects are less affected by drag relative to their weight.

What is the value of g on Earth?

The standard value of gravitational acceleration on Earth is 9.807 m/s² (often rounded to 9.8 m/s²). This means a falling object gains about 9.8 meters per second of speed for every second it falls. The exact value varies slightly depending on your location and altitude.

How do I calculate how long it takes an object to hit the ground?

Use the formula t = √(2h / g), where h is the height in meters and g is gravitational acceleration (9.807 m/s² on Earth). For example, dropping an object from 20 meters: t = √(2 × 20 / 9.807) = √(4.077) ≈ 2.02 seconds.

What is terminal velocity?

Terminal velocity is the fastest speed a falling object can reach when air resistance is present. It happens when the drag force pushing up equals the gravity pulling down, so the object stops speeding up and falls at a steady speed. For a skydiver in a spread-eagle position, terminal velocity is about 55 m/s (120 mph).

Why does the calculator show different results for different planets?

Each planet has a different gravitational acceleration because of differences in mass and size. For example, the Moon's gravity is only 1.622 m/s², while Jupiter's is 24.79 m/s². A stronger gravity means objects fall faster and hit the ground sooner, so the same drop height gives very different fall times and impact speeds on each planet.

What is the difference between positive and negative initial velocity?

A positive initial velocity means the object is thrown upward. It will rise, slow down, stop, then fall back down. A negative initial velocity means the object is thrown downward, so it starts falling even faster than if you just dropped it.

How is impact force calculated in this tool?

The calculator estimates impact force using F = m × v, assuming the object comes to a stop over 1 second. In real life, the stopping time is usually much shorter, which makes the actual impact force much larger. The result gives you a rough idea of the force involved.

Can I use this calculator for objects thrown horizontally?

No. This calculator only handles vertical free fall — objects dropped straight down or thrown straight up or down. If an object is launched at an angle or thrown sideways, you need a projectile motion calculator, which accounts for both horizontal and vertical movement.

What units can I use in this calculator?

You can use many common units. For height: meters, feet, kilometers, miles, inches, and centimeters. For time: seconds, milliseconds, and minutes. For velocity: m/s, km/h, mph, and ft/s. For mass: kilograms, grams, pounds, and ounces. For gravity: m/s², ft/s², and g-force.

What does the drag coefficient mean?

The drag coefficient is a number that describes how much air resistance an object creates based on its shape. A smooth, streamlined shape has a low drag coefficient (around 0.04 for a bullet), while a flat or irregular shape has a higher one (around 1.0–1.2 for a flat plate). A typical skydiver has a drag coefficient of about 0.7.

Why does the calculator say kinetic energy equals potential energy?

This is because of the law of conservation of energy. When there is no air resistance, all the potential energy (mgh) at the top converts into kinetic energy (½mv²) at the bottom. No energy is lost, so the two values are equal. With air resistance, some energy is lost to heat from drag, so kinetic energy at impact would be less.

How accurate is the air resistance calculation?

The air resistance mode gives an approximation. It uses a simplified model that assumes constant air density (1.225 kg/m³ at sea level) and a fixed drag coefficient. In real life, air density changes with altitude, and the drag coefficient can change with speed and orientation. For most basic estimates, the results are reasonable.

What is cross-section area and how do I find it?

Cross-section area is the size of the surface that faces the oncoming air as the object falls. Think of it as the shadow the object would cast if light shone straight up from below. For a sphere, it's π × r². For a person falling spread-eagle, it's about 0.7 m². For a person falling feet-first, it's much smaller, around 0.1–0.2 m².

How fast would I be going if I fell from 100 meters with no air resistance?

Using v = √(2 × g × h) = √(2 × 9.807 × 100) = √(1961.4) ≈ 44.3 m/s, which is about 159.5 km/h or 99.1 mph. The fall would take about 4.52 seconds.