Free Fall Calculator

Calculate the time of falling and the final speed of an object (or human) in free fall. Enter either the height (distance fallen) or the time and this calculator will determine the other and the final speed (assuming near-Earth gravity and neglecting air resistance; the calculator assumes the object is dropped from rest, v₀ = 0).

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Free Fall Formula

The formula to calculate the final velocity of an object in free fall (taking downward as positive) is:

 v = v₀ + g t 

• Where v is final velocity (m/s)
• v₀ is the initial velocity (m/s)
• g is the acceleration due to gravity (m/s²), approximately 9.81 m/s² near Earth’s surface
• t is total time (s)

If the object is dropped from rest (v₀ = 0), this simplifies to v = gt. (The direction/sign depends on your chosen coordinate system.)

In many introductory free-fall problems, the distance fallen (height) is known and the time is unknown. If the object is dropped from rest (v₀ = 0) and g is treated as constant, the time can be found with:

• where t is total time
• d is distance traveled (height fallen)
• g is the acceleration due to gravity

Free Fall Definition

Free fall is motion under the influence of gravity alone (i.e., with no other forces acting). In reality, air resistance is usually present, but many free-fall problems explicitly neglect it.

How to calculate free fall

Let’s look at an example of how to calculate the kinematic values of an object in free fall.

Let’s assume that you’re going on a skydiving adventure, but everything goes wrong! How long do you have to live before you hit the ground and how fast will you be going.

First, we will calculate the fall time. Let’s assume you’re jumping from a height of 10,000 meters and that you start from rest (v₀ = 0). Using t = √(2d/g) with g = 9.81 m/s², we get a total time of about 45.15 seconds.

Next, we calculate the final speed (in a vacuum). Using the time from above and v = gt, we get a final speed of about 442.9 m/s.

It should be noted that in a real-world application you would not be going so fast due to air resistance (and you would approach a terminal velocity). The formulas above assume a vacuum and constant g.

The following steps are required to calculate an object in free fall.

1. First, determine the vertical distance/height the object falls (displacement).
2. Second, determine the initial vertical velocity v₀ (often 0 if the object is dropped).
3. Last, choose an appropriate value for g (near Earth ≈ 9.81 m/s²) and use the kinematic equations (such as v = v₀ + gt and d = v₀t + ½gt²) to solve for time and final velocity.

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