Free fall is the motion of an object when gravity is the only force acting on it. Near Earth’s surface, gravity causes freely falling objects to accelerate downward at approximately 9.8 meters per second squared (m/s²), or 32.2 feet per second squared (ft/s²). This means an object’s downward velocity increases by about 9.8 m/s every second, provided no other forces significantly affect its motion.
Free fall helps explain why objects drop toward the ground, how projectiles move through the air, and why astronauts appear weightless while orbiting Earth. It is also a fundamental concept in classical mechanics, the branch of physics that describes the motion of objects and the forces that influence them.
Although people often associate free fall with an object simply dropping from a height, the concept has a broader meaning. An object thrown upward, a rock falling downward, and an astronaut in orbit can all be in free fall under the right conditions.
What does free fall mean in physics?
In physics, free fall occurs when gravity is the only force acting on an object. The object may be moving upward, moving downward, or following a curved path. What matters is not its direction of motion but the forces acting on it.
On Earth, air resistance often complicates free fall. A feather, for example, falls more slowly than a stone in ordinary air because air resistance has a much greater effect on the feather relative to its weight. However, if both objects fall in a vacuum, where there is no air to resist their motion, they accelerate at the same rate.
This distinction is important because everyday falling objects do not always demonstrate ideal free fall. In physics problems, free fall usually means that air resistance is negligible or absent, allowing gravity’s effect to be studied on its own.
Gravity is an attractive force between objects that have mass. Earth’s gravity pulls objects toward its center, which is why objects near the surface accelerate approximately vertically downward. The acceleration becomes slightly weaker at greater distances from Earth, although the change is small for ordinary heights near the ground.
Free fall is therefore not defined by an object being released from rest. It is defined by the absence of forces other than gravity.
What is acceleration due to gravity?
Acceleration due to gravity describes how quickly an object’s velocity changes under the influence of gravity. Near Earth’s surface, this acceleration is represented by the symbol g and has an approximate value of:
g = 9.8 m/s²
In U.S. customary units, the same acceleration is approximately:
g = 32.2 ft/s²
The standard acceleration due to gravity is sometimes given as 9.80665 m/s², a defined conventional value used in certain calculations. The actual local acceleration varies slightly with location, altitude, and other factors.
Acceleration is the rate at which velocity changes over time. An acceleration of 9.8 m/s² means that an object’s downward velocity increases by approximately 9.8 m/s during each second of free fall near Earth’s surface.
For example, suppose a ball is dropped from rest in a vacuum. After one second, its downward speed is approximately 9.8 m/s. After two seconds, its speed is approximately 19.6 m/s. After three seconds, its speed is approximately 29.4 m/s.
These values assume that g remains constant throughout the fall, which is a good approximation for ordinary heights near Earth’s surface.
Acceleration due to gravity is a vector quantity, meaning it has both magnitude and direction. If upward is defined as the positive direction, gravitational acceleration is written as −g. If downward is defined as positive, it is written as +g. The physical motion is the same; only the sign convention changes.
Why do objects of different masses fall at the same rate?
One of the most important principles of free fall is that objects fall with the same gravitational acceleration regardless of their mass, provided other forces are absent.
This result may seem counterintuitive. A heavy rock appears to fall faster than a light feather in everyday life. However, the difference is mainly caused by air resistance rather than mass alone.
Newton’s second law of motion states that an object’s acceleration equals the net force acting on it divided by its mass:
a = Fₙₑₜ / m
Near Earth’s surface, the gravitational force on an object is approximately:
Fᵍ = mg
Here, Fᵍ is the gravitational force, m is the object’s mass, and g is the acceleration due to gravity.
If gravity is the only force acting on the object, Newton’s second law becomes:
a = Fᵍ / m
Substituting the gravitational force gives:
a = mg / m = g
The mass cancels out, leaving the acceleration due to gravity.
This explains why a massive object and a lightweight object experience the same gravitational acceleration in a vacuum. A heavier object experiences a stronger gravitational force, but it also has proportionally greater inertia, meaning greater resistance to changes in motion. The two effects balance.
In ordinary air, however, the objects may fall differently because air resistance depends on factors such as shape, surface area, speed, and the properties of the air. A feather experiences substantial drag relative to its weight, while a compact metal ball generally experiences much less drag relative to its weight.
The main equations of free fall
Free-fall equations describe the relationship between an object’s position, velocity, acceleration, and elapsed time. They are particularly useful when gravitational acceleration can be treated as constant and air resistance can be ignored.
The equations below use the following symbols:
- v₀ = initial velocity
- v = final velocity
- g = acceleration due to gravity
- t = elapsed time
- y₀ = initial vertical position
- y = final vertical position
- Δy = vertical displacement
For consistency, assume upward is positive. Gravitational acceleration is then −g.
1. Velocity after a given time
The velocity of an object in free fall is:
v = v₀ − gt
This equation calculates the object’s velocity after a specified amount of time.
If an object is dropped from rest, its initial velocity is zero. The equation becomes:
v = −gt
The negative sign indicates downward motion under the chosen coordinate system. The object’s downward speed increases by approximately 9.8 m/s each second.
If the object is thrown upward, its initial velocity is positive. Gravity reduces its upward velocity until it reaches zero at the highest point, after which it begins moving downward.
2. Vertical displacement after a given time
The vertical displacement of an object under constant gravitational acceleration is:
Δy = v₀t − ½gt²
This equation determines how far an object moves vertically during a given interval.
For an object dropped from rest:
Δy = −½gt²
The displacement is negative because the object moves downward. Its downward distance traveled is:
d = ½gt²
This simplified form applies when the object starts from rest and falls without significant air resistance.
The equation shows that distance does not increase uniformly with time. Instead, the distance traveled grows with the square of the elapsed time. An object falling for twice as long travels four times the distance, assuming the same constant acceleration.
3. Velocity and displacement without time
Sometimes the elapsed time is unknown, but the initial velocity and vertical displacement are known. In that case, use:
v² = v₀² − 2gΔy
This equation connects velocity and displacement without requiring time as a variable.
For an object dropped from rest, the relationship between downward speed and downward distance is:
v² = 2gd
Taking the square root gives:
v = √(2gd)
Here, v represents the magnitude of the downward velocity, and d is the distance fallen.
4. Time required to fall from rest
The equation for displacement can also be rearranged to calculate the time required to fall a known distance.
Starting with:
d = ½gt²
Rearranging gives:
t² = 2d / g
Therefore:
t = √(2d / g)
This formula calculates the time required for an object dropped from rest to fall a vertical distance d, assuming constant gravitational acceleration and negligible air resistance.
The square root is necessary because distance increases with the square of time.
What happens to an object during free fall?
An object’s motion during free fall depends on its initial velocity. Gravity continuously changes its velocity, but the way that change appears depends on whether the object starts at rest, moves downward, or moves upward.
When an object is dropped from rest, it initially has zero velocity. Gravity immediately begins accelerating it downward. Its speed increases as it falls, and it covers progressively greater distances during equal intervals of time.
When an object is thrown downward, it begins with an initial downward velocity. Gravity increases its downward speed further. As a result, it generally reaches the ground sooner than an object released from rest at the same height, assuming both experience the same gravitational acceleration.
When an object is thrown upward, gravity acts against its initial upward motion. Its upward speed decreases steadily until it reaches the highest point of its trajectory. At that instant, its vertical velocity is zero. However, its acceleration is still downward at approximately 9.8 m/s².
The object then reverses direction and begins falling. As it descends, its downward speed increases.
The highest point is sometimes misunderstood as a place where gravity temporarily stops acting. In reality, gravity acts throughout the motion. The velocity becomes zero for an instant, but the acceleration does not.
If an object returns to its original height and air resistance is negligible, its speed at that height equals its initial speed. Its direction of motion is reversed, so its velocity has the same magnitude but the opposite sign.
Examples of free fall
Free-fall equations become easier to understand when applied to familiar situations. The following examples assume that air resistance is negligible and gravitational acceleration remains constant at 9.8 m/s².
Example 1: A ball dropped from a height
Suppose a ball is dropped from rest from a height of 20 meters. How long does it take to reach the ground, and how fast is it moving just before impact?
The known values are:
- Initial velocity: v₀ = 0 m/s
- Falling distance: d = 20 m
- Gravitational acceleration: g = 9.8 m/s²
To calculate the time, use:
t = √(2d / g)
Substitute the values:
t = √(2 × 20 / 9.8)
t = √4.08 ≈ 2.02 s
The ball takes approximately 2.02 seconds to reach the ground.
To calculate its impact speed, use:
v = √(2gd)
Substituting the values gives:
v = √(2 × 9.8 × 20)
v = √392 ≈ 19.8 m/s
The ball reaches the ground at approximately 19.8 m/s, or about 71 km/h.
These results describe idealized motion. In an actual fall, air resistance and the ball’s shape may slightly change the impact speed and fall time.
Example 2: Finding the speed after three seconds
Imagine an object dropped from rest that has been falling freely for three seconds. What is its downward speed?
Use the velocity equation:
v = v₀ − gt
Since the object starts from rest, v₀ = 0. Substituting the values gives:
v = 0 − (9.8 × 3)
v = −29.4 m/s
The negative sign indicates downward motion. The object’s speed is therefore 29.4 m/s.
This result illustrates the meaning of gravitational acceleration: after three seconds of ideal free fall, an object released from rest reaches a downward speed of approximately 29.4 m/s.
Example 3: An object thrown upward
Suppose a ball is thrown vertically upward at an initial speed of 19.6 m/s. How long does it take to reach its highest point, and how high does it rise above its starting position?
At the highest point, the ball’s vertical velocity is zero.
Using the velocity equation:
v = v₀ − gt
Set v = 0:
0 = 19.6 − 9.8t
Rearranging gives:
t = 19.6 / 9.8 = 2 s
The ball takes two seconds to reach its highest point.
To calculate its maximum height above the starting position, use:
Δy = v₀t − ½gt²
Substitute the values:
Δy = (19.6 × 2) − ½(9.8 × 2²)
Δy = 39.2 − 19.6 = 19.6 m
The ball rises approximately 19.6 meters above its starting position.
At the highest point, its vertical velocity is zero, but gravity continues to accelerate it downward. If air resistance is negligible, the ball takes another two seconds to return to its original height.
Example 4: Comparing two objects in a vacuum
Imagine dropping a steel ball and a wooden ball simultaneously from the same height inside a vacuum chamber. Both begin at rest.
Because gravity is the only significant force acting on either ball, both accelerate downward at approximately 9.8 m/s². They also have the same initial velocity and fall through the same vertical distance.
Accordingly, both take the same amount of time to reach the bottom and have the same speed immediately before arriving.
Their masses do not change this result. In a vacuum, the difference in mass affects the gravitational force on each object, but it does not affect the acceleration due to gravity near Earth’s surface.
This experiment illustrates the distinction between ideal free fall and falling through air.
How does air resistance affect free fall?
Air resistance, also called drag, is a force that opposes an object’s motion relative to the surrounding air. Unlike gravity, which pulls an object toward Earth, air resistance acts against the object’s movement through the air.
When an object first begins falling from rest, its speed is low, so air resistance is often relatively small. Gravity produces a net downward force, causing the object to accelerate.
As the object speeds up, air resistance generally increases. The upward drag force reduces the net downward force, so the object’s acceleration becomes smaller than g.
Eventually, a falling object may reach terminal velocity. This is the constant speed reached when upward air resistance balances downward gravitational force. At that point, the net force is zero, so the object no longer accelerates.
Terminal velocity depends on several factors, including the object’s mass, shape, cross-sectional area, orientation, and the density of the surrounding air. A compact, heavy object may reach a much higher terminal velocity than a lightweight object with a large surface area relative to its mass.
For example, a flat sheet of paper usually falls more slowly than a tightly crumpled sheet of the same paper. The flat sheet experiences greater air resistance relative to its weight, while the crumpled sheet moves through the air more easily.
Air resistance can also cause objects to reach the ground at different times even when they begin falling together. Consequently, the standard free-fall equations should not be applied without adjustment when drag has a substantial effect.
Is an object thrown upward also in free fall?
Yes. An object thrown upward is in free fall once it leaves the thrower’s hand, provided gravity is the only significant force acting on it.
Although the object initially moves upward, gravity accelerates it downward throughout its flight. This means its upward velocity steadily decreases until it reaches zero at the highest point.
Afterward, the object accelerates downward and gains speed as it falls.
The important distinction is between velocity and acceleration. Velocity describes an object’s speed and direction of motion, while acceleration describes how its velocity changes. An object can move upward while accelerating downward because its upward velocity is decreasing.
At the highest point, the object’s instantaneous vertical velocity is zero, but its acceleration remains approximately 9.8 m/s² downward.
This principle also explains why a ball thrown upward follows a curved path when it has horizontal motion. In ideal projectile motion, gravity changes the vertical component of velocity while the horizontal component remains constant. The object follows a parabolic trajectory when air resistance is negligible and gravity is approximately uniform.
Is an astronaut in orbit in free fall?
An astronaut orbiting Earth is in continuous free fall, even though the astronaut may appear to float inside a spacecraft.
Gravity does not disappear in orbit. Instead, gravity continuously accelerates the spacecraft and everything inside it toward Earth. The spacecraft also has substantial sideways velocity, so as it falls toward Earth, the planet’s curved surface drops away beneath its path.
The result is an orbit: the spacecraft continually falls around Earth rather than striking the ground.
The astronaut and spacecraft experience nearly the same gravitational acceleration. Because both are falling together, the astronaut does not normally feel the supporting force that a person standing on the ground experiences. This condition produces the sensation of weightlessness.
Weightlessness in orbit therefore does not mean the absence of gravity. It means that the astronaut and surrounding spacecraft are in a state of free fall together, with little or no support force acting on the astronaut.
The same principle applies to an object inside a freely falling elevator. If the elevator and the object accelerate downward together, the object may appear to float relative to the elevator. In a real elevator, however, safety systems and other forces complicate the situation, and a person should never attempt to test this effect.
How does free fall differ on other planets?
The acceleration due to gravity varies from one celestial body to another because gravitational acceleration depends on the body’s mass and the distance from its center.
For an approximately spherical body, the gravitational acceleration outside it is described by:
g = GM / r²
Here, G is the universal gravitational constant, M is the mass of the celestial body, and r is the distance from its center.
Near the surface, r is approximately equal to the body’s radius. A planet’s surface gravity therefore depends on both its mass and its radius.
A more massive planet does not necessarily have stronger surface gravity than a less massive one, because a larger radius increases the distance from the planet’s center. Both quantities matter.
For example, the Moon has weaker surface gravity than Earth. An object dropped near the lunar surface accelerates downward at approximately 1.6 m/s², compared with about 9.8 m/s² near Earth’s surface.
As a result, an object dropped from the same height on the Moon takes longer to reach the ground than it would on Earth, assuming negligible air resistance.
Mars also has weaker surface gravity than Earth, at approximately 3.7 m/s². An object in ideal free fall near the Martian surface therefore gains downward speed more slowly than it does near Earth’s surface.
These differences affect the motion of dropped objects, projectiles, and spacecraft. The same basic equations apply, but the value of g must be adjusted for the local gravitational field when it can be treated as constant.
Common misconceptions about free fall
Several common misunderstandings arise from confusing everyday falling motion with the idealized conditions used in physics.
Free fall does not require an object to start from rest. An object can be dropped, thrown upward, or thrown downward and still be in free fall if gravity is the only significant force acting on it.
Heavier objects do not inherently fall faster than lighter objects. In a vacuum, objects near Earth’s surface have the same gravitational acceleration regardless of mass. Differences in ordinary air usually result from drag.
Gravity does not stop at the highest point of an object’s trajectory. An upward-moving object has zero vertical velocity for an instant at its highest point, but its acceleration remains downward.
Weightlessness does not mean gravity is absent. Astronauts in orbit experience apparent weightlessness because they and their spacecraft are falling together under gravity.
Acceleration due to gravity is not the same as gravitational force. Gravitational force depends on an object’s mass, while its acceleration under gravity near Earth’s surface is approximately the same as that of other objects, provided other forces are negligible.
Understanding these distinctions makes it easier to apply free-fall equations correctly and interpret the motion of objects in both everyday and astronomical settings.
Why free fall matters in physics
Free fall provides one of the clearest ways to study the relationship between force, acceleration, velocity, and displacement. By examining objects under the influence of gravity alone, physicists can predict how motion changes over time and identify the effects of other forces.
The concept is essential to understanding projectile motion, falling objects, orbital mechanics, and the behavior of objects in gravitational fields. It also demonstrates a central principle of mechanics: an object’s motion depends on the net force acting on it, not simply on its mass or its direction of travel.
The key ideas are straightforward. Near Earth’s surface, an object in ideal free fall accelerates downward at approximately 9.8 m/s². Its velocity changes steadily with time, and its displacement depends on both its initial velocity and the time spent falling. When air resistance is significant, the motion becomes more complex, and the ideal equations must be modified.
With these principles, free fall becomes more than the simple act of dropping an object. It becomes a practical model for understanding how gravity shapes motion on Earth and throughout the universe.