Free Fall Calculator

About the Free Fall Calculator

In free fall an object accelerates downward under gravity alone. From the fall time you can find how far it falls and how fast it is moving when it lands (ignoring air resistance).

Enter the fall time in seconds and gravity (default 9.81 m/s²). The tool returns both the distance fallen and the final velocity.

How to use this calculator

1. Enter the time of fall in seconds, using a positive number.
2. Choose the value of gravity, usually 97.8\,\text{m/s}^297.8\,\text{m/s}^2 on Earth if your tool allows it.
3. Read the distance fallen and final velocity from the results.
4. Check that your units are consistent, so time is in seconds and distance is in meters.

The formula explained

The formula for distance, \(d = \tfrac{1}{2}gt^2\), computes how far an object falls after time \(t\). The formula for velocity, \(v = gt\), computes the object'

• d = distance fallen in meters
• g = acceleration due to gravity in meters per second squared
• t = time of fall in seconds
• v = final velocity in meters per second

Step by step method

1. Start with the time \(t\) and the gravity value \(g\).
2. Compute the distance with \(d = \tfrac{1}{2}gt^2\).
3. Compute the final velocity with \(v = gt\).

Worked example

Problem. A stone falls for \(3\) seconds on Earth. Find the distance fallen and the final velocity, using \(g = 9.8\,\text{m/s}^2\).

1. Substitute into the distance formula, \(d = \tfrac{1}{2}(9.8)(3^2)\).
2. Calculate \(3^2 = 9\), so \(d = 4.9 \times 9 = 44.1\,\text{m}\).
3. Use the velocity formula, \(v = (9.8)(3) = 29.4\,\text{m/s}\).

Tips and common mistakes

• Use \(9.8\,\text{m/s}^2\) for Earth unless the problem gives a different value of gravity.
• Do not forget to square the time in \(d = \tfrac{1}{2}gt^2\), because \(t^2\) is not the same as \(2t\).

Frequently asked questions