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.