Work out the motion of an object in free fall. Enter either the time of fall or the height it drops (leave the other blank), set the initial velocity and gravity if you need to, and the calculator finds the time, distance fallen, and final velocity.
The free fall calculator works out how a falling object moves under gravity. Give it the time of the fall or the height of the drop — along with an optional starting speed and the strength of gravity — and it returns the time of fall, the distance fallen, and the final velocity at impact. It is the go-to tool for physics homework, for satisfying curiosity about how fast something hits the ground, and for understanding one of the most fundamental kinds of motion in the universe.
Free fall is the motion of an object when the only force acting on it is gravity. On Earth, gravity accelerates every falling object at the same rate regardless of its mass — a famous fact first demonstrated by Galileo. This calculator applies the standard equations of motion for constant acceleration, so you can predict exactly where a falling object will be and how fast it will be moving at any moment.
Free fall is any motion where gravity is the only force at work. An apple dropping from a tree, a diver leaving a platform, and a skydiver in the first moments before air resistance builds up are all in (approximately) free fall. The defining feature is that the object accelerates downward at a constant rate, g, and — in the idealized case this calculator models — nothing else, such as air resistance, slows it down.
A key and often surprising point is that in free fall, mass does not matter. A feather and a hammer dropped in a vacuum hit the ground at exactly the same time, because gravity gives every object the same acceleration. The calculator therefore never asks for the object's weight — it is irrelevant to the physics of the fall.
Free fall is a case of motion with constant acceleration, so it obeys the standard kinematic equations. With g for gravitational acceleration, v₀ for the initial (starting) velocity, t for time, h for the distance fallen, and v for the final velocity:
v = v₀ + g × t
h = v₀ × t + ½ × g × t²
v = √(v₀² + 2 × g × h)
When the object simply drops from rest, the initial velocity is zero and the equations simplify to the familiar forms:
v = g × t
h = ½ × g × t²
t = √(2h ÷ g)
The calculator rearranges these depending on whether you give it the time or the height, so you always get the complete picture of the fall from a single input.
The value g is the acceleration that gravity gives to a falling object. On Earth's surface, the standard value is 9.80665 m/s² (about 32.174 ft/s²), meaning a falling object speeds up by roughly 9.81 meters per second every second. The calculator uses this as the default, but you can change it — useful for physics problems set on the Moon (about 1.62 m/s²), on Mars (about 3.71 m/s²), or anywhere gravity differs. Because g is an acceleration, its units are distance per second squared: m/s² in metric, ft/s² in imperial.
Suppose an object is dropped from rest (v₀ = 0) and falls for 8 seconds under Earth's gravity. Using the formulas:
So after 8 seconds the object is moving at about 78.45 m/s (roughly 282 km/h) and has fallen about 313.8 meters. Running it the other way — entering a height of 313.8 m — returns a fall time of 8 seconds and the same final velocity, confirming the calculation in both directions.
Not every fall starts from rest. If you throw a ball straight down, it already has a downward speed the instant it leaves your hand, and that initial velocity adds to the effect of gravity. The calculator handles this through the v₀ field: enter the starting downward speed and the equations v = v₀ + gt and h = v₀t + ½gt² account for it automatically. For example, an object thrown down at 5 m/s that then falls for 3 seconds reaches 5 + 9.80665 × 3 ≈ 34.4 m/s and travels 5 × 3 + ½ × 9.80665 × 9 ≈ 59.1 m. Setting v₀ to zero recovers the pure "dropped from rest" case.
This calculator models idealized free fall, ignoring air resistance (drag). In reality, as an object speeds up, air pushes back harder, and eventually the drag force balances gravity so the object stops accelerating — it has reached terminal velocity. A skydiver, for instance, reaches a terminal velocity of around 53 m/s (about 190 km/h) in a belly-down position, far less than the ever-increasing speed the free fall equations predict. For dense, compact objects falling short distances — a stone dropped down a well, a ball off a building — air resistance is small and the idealized results are very accurate. For light or long falls, treat the calculator's velocity as an upper bound that the real object will not exceed once drag takes hold.
Because gravity differs from place to place, the same drop plays out very differently across the solar system. On the Moon, where g is only about 1.62 m/s², an object dropped for 8 seconds reaches just under 13 m/s and falls about 52 m — roughly a sixth of the Earth values, which is why astronauts moved in slow, floating bounds. On Mars (g ≈ 3.71 m/s²) things fall noticeably faster than on the Moon but still far more gently than on Earth. On Jupiter, with g around 24.79 m/s², objects plummet more than twice as fast as on Earth. By changing the gravity field in this calculator you can explore any of these scenarios and build an intuition for how gravity shapes motion — a favorite exercise in physics classrooms.
It is worth clarifying what this calculator does and does not cover. Free fall, as modeled here, is purely vertical motion: an object dropped straight down or thrown straight down, moving only up and down under gravity. Projectile motion — a ball thrown at an angle, a cannonball, a long jump — is more general, combining a horizontal velocity that stays constant with a vertical motion that is exactly the free fall this calculator computes. In other words, free fall is the vertical "half" of every projectile's flight. If you drop one ball and simultaneously fire another horizontally from the same height, both hit the ground at the same instant, because their vertical motion is identical free fall regardless of the horizontal speed. That famous result — sometimes shown in classrooms with a spring-loaded "monkey and hunter" demonstration — follows directly from the equations on this page. For straight-down drops and throws, the results here are exact; for angled throws, use them for the vertical component and add the horizontal motion separately.
Because velocity in free fall grows steadily with time, a short reference table gives a good feel for how quickly speed builds up on Earth (from rest, ignoring air resistance):
Notice a striking pattern: while the velocity grows in equal steps each second (linearly), the distance grows with the square of time, so it climbs much faster — doubling the fall time quadruples the distance. This is why a fall from twice the height does not take twice as long, and why falls from great heights become dangerous so quickly. The calculator captures this relationship exactly, letting you see how a one-second difference in fall time translates into a large difference in both speed and distance.
One classic use of the free fall equations is estimating how deep or how high something is by timing a dropped object. If you drop a stone into a well and it takes 2 seconds to hit the bottom, the depth is approximately h = ½ × 9.80665 × 2² ≈ 19.6 meters. Drop a pebble from a bridge and count 3 seconds until the splash, and the bridge is roughly 44 meters above the water. This trick works best for shorter drops where air resistance is small and where you can time the fall accurately — and it is worth remembering that for longer drops you should also account for the time it takes the sound to travel back up, which this idealized calculator does not include. Even so, for a quick field estimate, timing a fall and entering it here is a surprisingly effective way to gauge a height you cannot easily measure directly. It is the same principle scientists use, in far more precise forms, to measure everything from cliff heights to the local strength of gravity.
For an object dropped from rest, the velocity after time t is v = g × t and the distance fallen is h = ½ × g × t². With an initial downward velocity v₀, use v = v₀ + gt and h = v₀t + ½gt².
Multiply the gravitational acceleration by the time (and add any initial velocity): v = v₀ + g × t. After 8 seconds from rest on Earth, that is 9.80665 × 8 ≈ 78.45 m/s.
No. In free fall (ignoring air resistance), all objects accelerate at the same rate regardless of mass. A feather and a hammer fall together in a vacuum. That is why this calculator does not ask for the object's mass.
The standard gravitational acceleration at Earth's surface is 9.80665 m/s² (about 32.174 ft/s²). You can change it in the calculator to model the Moon, Mars, or any other gravity.
Use h = ½ × g × t² for a drop from rest. If you know how long something fell, this gives the distance. This calculator does it automatically when you enter the time.
No. It models idealized free fall with gravity as the only force. Real falls are slowed by air resistance and level off at terminal velocity, so the calculator's speeds are an upper limit for long or light-object falls.
This Free Fall Calculator is provided for educational and general informational purposes. It models idealized free fall (no air resistance) using the standard kinematic equations. Real-world results differ due to drag and other factors; do not use it for safety-critical decisions.