Free Fall Calculator (Time, Speed and Height)
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Other tools you may find usefulFree fall calculator - uniformly accelerated motion in physics
Free fall is one of the most fundamental processes studied in classical physics and mechanics. It is defined as the movement of a falling body solely under the influence of gravity, completely disregarding air resistance (i.e. movement taking place in a vacuum). The famous physicist Galileo Galilei was the first to prove that in a vacuum all bodies - regardless of their mass - fall to the earth with exactly the same acceleration. Near the Earth's surface, this acceleration is on average 9.81 m/s² and is denoted by the symbol $g$. Our free online free fall calculator allows you to calculate fall time, final velocity and initial height in seconds if you know at least one of these parameters.
With this tool, you can quickly verify your physics homework, understand time-velocity relationships in uniformly accelerated motion, and conduct simulations for other planets in the solar system.
Physical formulas used in free fall calculations
The motion of bodies in free fall is described by the classical kinematic equations for uniformly accelerated motion with an initial velocity equal to zero ($v_0 = 0$). Below are the most important mathematical relationships:
- Final velocity ($v$):The speed that the body reaches just before it hits the ground. $$v = g \cdot t \quad \text{or} \quad v = \sqrt{2 \cdot g \cdot h}$$
- Height / Falling distance ($h$):The distance a body travels in a given time. $$h = \frac{g \cdot t^2}{2} \quad \text{or} \quad h = \frac{v^2}{2 \cdot g}$$
- Falling time ($t$):The time it takes to cover a given height. $$t = \frac{v}{g} \quad \text{or} \quad t = \sqrt{\frac{2 \cdot h}{g}}$$
Where: $h$ is the height (m), $v$ is the final velocity (m/s), $t$ is the time (s), and $g$ is the acceleration due to gravity ($9.80665 \text{ m/s}^2$).
Summary of fall parameters for various initial heights
The table below shows the calculated values for fall time and final velocity (in both meters per second and kilometers per hour) for example heights on Earth ($g = 9.81 \text{ m/s}^2$):
| Initial height (m) | Fall time (s) | Final speed (m/s) | Final speed (km/h) | Kinetic energy per 1 kg of mass (J) |
|---|---|---|---|---|
| 1 m | 0.45 s | 4.43 m/s | 15.9 km/h | 9.8 J |
| 5 m | 1.01 s | 9.90 m/s | 35.6 km/h | 49.1 J |
| 10 m (3rd floor equivalent) | 1.43 s | 14.01 m/s | 50.4 km/h | 98.1 J |
| 50 m | 3.19 s | 31.32 m/s | 112.8 km/h | 490.5 J |
| 100 m | 4.52 s | 44.29 m/s | 159.5 km/h | 981.0 J |
| 500 m | 10.10 s | 99.05 m/s | 356.6 km/h | 4905.0 J |
How to use the free fall calculator? Instruction
To perform calculations in our calculator, simply follow these steps:
- Select a planet or enter gravity:By default, the calculator uses acceleration due to gravity ($9.81 \text{ m/s}^2$). However, you can choose another object, such as the Moon ($1.62 \text{ m/s}^2$) or Mars ($3.71 \text{ m/s}^2$).
- Enter a known value:Enter one of the known values: height (distance), fall time, or final velocity.
- Confirm by clicking the button:Click the "Calculate" button and the system will automatically complete the remaining fields and present the results with units.
Frequently Asked Questions (FAQ)
Why do heavy objects sometimes fall faster than light objects in the real world?
In real conditions on Earth, the movement of bodies is slowed down by air resistance (friction). The resistance force depends on the shape and surface of the body. Light objects with a large surface area (e.g. a feather or a piece of paper) experience strong air resistance, which quickly balances the force of gravity. Heavy, aerodynamic objects (e.g. a steel ball) overcome this resistance more easily. In a vacuum, the feather and the ball will fall at exactly the same moment.
What is terminal velocity?
Terminal velocity is the maximum speed that a falling body can achieve in the atmosphere. It occurs when the force of air resistance becomes equal to the force of gravity acting on the body. From this moment, the body falls with uniform motion (without acceleration). For a falling person in a stable position (belly down), the terminal velocity is approximately 200 km/h.
Does body weight have any effect on free fall?
In the definition of free fall (in a vacuum), the body's mass has absolutely no effect on the speed or time of falling. Physical formulas do not contain a variable for mass ($m$). Time and speed depend solely on altitude and gravity.
What is the value of gravitational acceleration on other planets?
The acceleration due to gravity depends on the mass and radius of the given celestial body. Gravity on the Moon is about 6 times weaker than on Earth ($1.62 \text{ m/s}^2$). On Mars it is $3.71 \text{ m/s}^2$, while on Jupiter the gravity is powerful and reaches $24.79 \text{ m/s}^2$. This means that on Jupiter you would fall more than twice as fast.
What happens during a free fall in an elevator?
If the elevator breaks and begins to fall in free fall with the acceleration due to gravity $g$, those inside will experience a state of weightlessness. They will float in the air relative to the elevator car because they are falling with exactly the same speed and acceleration as it. This state is used to train cosmonauts in special planes performing parabolic flights.