3.1928
s
50
m
31.3209
m/s
112.7553
km/h
15.6605
m/s
31.3209
kg·m/s
490.5
J
3.1928
s
50
m
31.3209
m/s
112.7553
km/h
15.6605
m/s
31.3209
kg·m/s
490.5
J
The Free Fall Calculator analyzes the motion of an object falling under the sole influence of gravity, with no air resistance. Free fall is one of the most fundamental examples of uniformly accelerated motion and has been studied since Galileo’s famous experiments at the Leaning Tower of Pisa in the late 16th century.
In free fall, every object—regardless of its mass—accelerates toward the Earth at the same rate, approximately 9.81 m/s² (commonly denoted as g). This was a revolutionary insight that contradicted the Aristotelian view that heavier objects fall faster. Apollo 15 astronaut David Scott famously demonstrated this on the Moon by dropping a hammer and a feather simultaneously; both hit the lunar surface at the same time in the airless environment.
This calculator offers two modes. In the first mode, you provide the height from which the object falls, and the calculator determines the time it takes to reach the ground and its velocity at impact. In the second mode, you enter the time of fall, and the calculator computes the distance fallen and the velocity reached. Both modes assume the object starts from rest (zero initial velocity) and falls without air resistance.
The mathematics of free fall are beautifully simple. The three key equations are: h = ½gt² (height as a function of time), v = gt (velocity as a function of time), and v² = 2gh (velocity as a function of height). From any one known quantity, all others can be derived. These equations are special cases of the general SUVAT equations with initial velocity equal to zero and acceleration equal to g.
Free fall physics has numerous practical applications. Skydivers use free fall calculations to plan their jumps (though they must also account for air resistance at high speeds). Engineers design drop tests for product safety, calculating impact velocities for various drop heights. Geophysicists measure the local value of g to map variations in Earth’s gravitational field, which reveals information about subsurface geological structures. In sports, free fall calculations help analyze the flight of balls, divers, and gymnasts during airborne phases.
The gravitational acceleration value of 9.81 m/s² is an average for Earth’s surface. The actual value varies slightly with latitude (from about 9.78 m/s² at the equator to 9.83 m/s² at the poles) and altitude. For other celestial bodies, g is very different: 1.62 m/s² on the Moon, 3.72 m/s² on Mars, and 24.79 m/s² on Jupiter. You can adjust the g value in the advanced settings to model free fall on any planet.
Free fall equations assume zero initial velocity and constant gravitational acceleration g:
Given height, find time and velocity:
$$t = \sqrt{\frac{2h}{g}}$$
$$v = \sqrt{2gh}$$
Given time, find height and velocity:
$$h = \frac{1}{2} g t^2$$
$$v = g t$$
Average velocity during free fall from rest:
$$\bar{v} = \frac{v}{2} = \frac{gt}{2}$$
These equations are derived from the general kinematic equations with v₀ = 0 and a = g.
The results show the fall time in seconds, the impact velocity in both m/s and km/h, the fall height in meters, and the average velocity during the fall. For perspective, an object dropped from 5 m hits the ground at about 9.9 m/s (35.6 km/h) after 1.01 seconds. From 50 m, the impact speed is 31.3 m/s (113 km/h) after 3.19 seconds. In reality, air resistance becomes significant at higher speeds, so these are theoretical maximum values.
Inputs
Results
A stone is dropped from a 45-meter bridge. It takes 3.03 seconds to hit the water and reaches an impact velocity of 29.7 m/s (107 km/h).
Inputs
Results
An object in free fall for 4 seconds drops 78.48 meters and reaches a velocity of 39.24 m/s (141.3 km/h). In reality, air resistance would reduce these values.
In the absence of air resistance, all objects fall at the same rate regardless of mass. This is because gravitational force is proportional to mass (F = mg), and by Newton’s second law (F = ma), the mass cancels out: a = F/m = mg/m = g. Heavier objects experience more gravitational force, but they also have more inertia, so the acceleration is identical.
The calculator is highly accurate for short drops, dense objects, or vacuum conditions. For long falls or light objects (feathers, paper), air resistance becomes significant and the calculator overestimates the velocity. At terminal velocity, air drag equals gravity and acceleration drops to zero—this effect is not modeled here.
Terminal velocity is the maximum speed a falling object reaches when air resistance equals the gravitational force. At this point, acceleration becomes zero and the object falls at constant speed. For a human skydiver, terminal velocity is about 53 m/s (190 km/h) in a spread-eagle position and 90 m/s (320 km/h) in a head-down dive.
Yes. Expand the advanced settings and change the gravitational acceleration (g) to the value for the desired body. Common values: Moon = 1.62 m/s², Mars = 3.72 m/s², Jupiter = 24.79 m/s², Venus = 8.87 m/s². The calculator will adjust all results accordingly.
This free fall calculator assumes the object starts from rest (v₀ = 0). If there is an initial downward velocity, use the Displacement Calculator instead, setting the initial velocity and acceleration to 9.81 m/s². If the object is thrown upward, the problem becomes projectile motion in one dimension.
Galileo performed inclined plane experiments around 1604, using ramps to slow down the acceleration and make it measurable with the timekeeping devices of his era. He demonstrated that the distance traveled was proportional to the square of the time, consistent with constant acceleration independent of mass. The famous Tower of Pisa experiment is likely apocryphal but captures the spirit of his discoveries.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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