Free Fall Calculator Formula
Understand the math behind the free fall calculator. Each variable explained with a worked example.
Formulas Used
Distance Fallen
distance = 0.5 * gravity * pow(time, 2)Final Velocity
final_velocity = gravity * timeVariables
| Variable | Description | Default |
|---|---|---|
gravity | Gravitational Acceleration(m/s²) | 9.81 |
time | Time of Fall(s) | 3 |
How It Works
Free Fall Under Gravity
An object released from rest near Earth's surface accelerates uniformly downward.
Formulas
d = (1/2) * g * t²
v_f = g * t
These assume no air resistance and zero initial velocity.
Worked Example
A stone is dropped from a tall building and falls for 3 seconds.
- 01d = 0.5 * g * t²
- 02d = 0.5 * 9.81 * 9
- 03d = 44.145 m
- 04v_f = g * t = 9.81 * 3 = 29.43 m/s
When to Use This Formula
- Calculating how long it takes an object to fall from a known height, such as estimating the drop time from a bridge or building for a physics problem.
- Determining the velocity an object reaches just before impact after falling from rest, which is critical for safety engineering and impact analysis.
- Estimating the height of a cliff or structure by timing how long a dropped stone takes to hit the ground.
- Designing drop-test experiments in product testing where you need to know the impact speed at a specific drop height.
- Solving introductory physics problems involving objects dropped from rest under uniform gravitational acceleration.
Common Mistakes to Avoid
- Using g = 9.8 m/s² when the problem uses feet — in imperial units, g = 32.2 ft/s². Mixing metric g with imperial distances gives results that are off by a factor of about 3.28.
- Forgetting that free fall equations assume no air resistance — for light or large-surface-area objects (feathers, parachutes, paper), air drag is significant and terminal velocity is reached well before the speed these formulas predict.
- Confusing height with distance in the formula h = ½gt² — h is the distance fallen from the starting point, not the remaining height above the ground. If you want height above ground, subtract the fallen distance from the initial height.
- Neglecting that the formulas assume the object starts from rest — if the object has an initial velocity (thrown downward or upward), you must use v = v₀ + gt and h = v₀t + ½gt² instead of the simplified versions.
Frequently Asked Questions
Does mass affect free fall distance?
No. In the absence of air resistance, all objects fall at the same rate regardless of mass, as demonstrated by Galileo.
What is the value of g on Earth?
The standard gravitational acceleration on Earth is approximately 9.81 m/s², varying slightly by location and altitude.
How does air resistance change things?
Air resistance opposes motion and increases with speed. Eventually the drag force equals gravity, and the object reaches terminal velocity.
Learn More
Guide
How to Calculate Velocity and Acceleration
Learn how to calculate velocity and acceleration step by step. Covers average and instantaneous velocity, uniform acceleration, kinematic equations, and worked examples.
Ready to run the numbers?
Open Free Fall Calculator