This all-in-one online Free Fall Calculator performs calculations using formulas that relate the initial velocity (v0), final velocity (v), time (t), and height (h) of free fall of an object in the gravitational field of a planet with the known free fall acceleration (or gravitational acceleration g). The resistance of the planet’s atmosphere is completely ignored in this case.
To perform the calculations, you must first specify the acceleration of free fall (the default value is the acceleration at the Earth’s surface). Then it is necessary to enter the known values of any two parameters specified above. After clicking the Calculate button, the values of the other two parameters are obtained.
It is important to clarify that the coordinate axis of distances (and velocities) is directed downwards, i.e. towards the surface of the planet (see figure below). So, for example, a body thrown upwards will have a negative initial velocity and will travel a negative path upwards before it starts to fall onto the surface of the planet.
v = v0 + g·t; h = v0·t + g·t2/2
What is Free Fall?
Free fall is the motion of an object under the influence of gravity alone, without any other forces acting upon it, such as air resistance. In an idealized vacuum, all objects, regardless of their mass, will fall at the same rate when subjected to gravity. This principle was famously demonstrated by Galileo Galilei, who theorized that a feather and a cannonball would hit the ground at the same time in the absence of air resistance.
In real-world conditions, however, air resistance affects objects differently depending on their shape, mass, and surface area. Nevertheless, free fall calculations typically assume a vacuum or negligible air resistance to simplify the analysis. Our calculator completely neglects atmospheric resistance.
Another important requirement that we take into account in our calculations is the constancy of the gravitational force acting on the object. This is true for the motion of bodies near the surface of the planet, i.e. at distances from the surface much smaller than the radius of the planet.
Free Fall Velocity
The velocity of an object in free fall increases as it continues to descend due to the constant acceleration caused by gravity. This acceleration, denoted as \(g\), has a standard value of approximately \(9.80665 \ m/s^2\) on the surface of Earth.
The velocity of an object in free fall at any given time can be determined using the equation:
$$v = v_0 + g \cdot t$$
where:
• \(v_0\) is the initial velocity,
• \(v\) is the velocity at time \(t\),
• \(t\) is the time the object has been falling.
This equation, like the equation below, is of scalar form. This means that we consider only one-dimensional motion along the direction of gravity.
On the space-time diagram of free fall shown here, the axis of distances (and velocities) is directed downwards, i.e. in the direction of gravity. That is why the equations we use in our calculator have a plus sign before the acceleration of free fall.
Free Fall Distance
The distance an object travels in free fall is determined using the kinematic equation:
$$h = v_0 \cdot t + \frac{1}{2} \cdot g \cdot t^2$$
where:
• \(h\) is the distance travelled,
• \(v_0\) is the initial velocity,
• \(t\) is the time the object has been moving.
Examples of Using the Calculator
Below we provide some examples of using our calculator.
Example 1. A body at rest at a height of 100 m from the Earth’s surface falls freely to its surface. After what time will the body reach the Earth’s surface and what will be the velocity of the body?
By entering \(v_0 = 0 \ m/s\) and \(h = 100 \ m\) into the fields of our calculator, we will get \(t = 4.51601 \ s\) and \(v = 44.28691 \ m/s\) as a result.
Example 2. A body is thrown upward with an initial velocity of 12 m/s. What will be the velocity of the body and at what height above the Earth’s surface will it be 2 seconds after the throw?
Obviously, we must enter the values of the initial velocity of the body and the time of its motion into the corresponding fields of our free fall calculator. Taking into account the conditions of the problem, we enter \(v_0 = -12 \ m/s\) and \(t = 2 \ s\). A negative value of the initial velocity means that the body was thrown up, i.e. began to move in the direction opposite to the direction of the velocity axis.
By clicking the Calculate button, we get the result: \(v = 7.6133 \ m/s\) and \(h = -4.3867 \ m\). A negative value of the height means that \(2\) seconds after the throw, the body will be higher than its initial location. And a positive value of its velocity at this moment means that the body is already moving down.
Example 3. Solve the same problem as in Example 1, but for Mars. Compare the results obtained with those obtained for the Earth.
As in Example 1, we enter \(v_0 = 0 \ m/s\) and \(h = 100 \ m\) into the fields of our calculator. But now we also need to specify the value of the free fall acceleration on the surface of Mars. This value can be taken from the table below. From the table, it is clear that this acceleration is only \(0.3895\) of the Earth’s acceleration. That is, by choosing \(g\) as the unit of measurement, we insert \(0.3895\) into the acceleration field.
By clicking the Calculate button, we get the result: \(t = 7.23604 \ s\) and \(v = 27.63943 \ m/s\). As we can see, the body needs significantly more time to fall on the surface of Mars and at the moment of falling it has a lower velocity. All these are obvious consequences of the weaker gravity field of Mars compared to Earth.
Comparative Gravities of Planets
The table below shows comparative gravitational accelerations at the surface of the Sun, the Earth’s moon, and big planets in the Solar System.
Related calculators
Check out our other physics calculators such as Gravitational Force Calculator or Kinetic Energy Calculator.