Welcome to the Height to Velocity Calculator! This tool helps you determine the final speed of an object falling freely from a certain height under gravity. Whether you’re a physics student, teacher, or simply curious about motion, this calculator makes the process simple and accurate.
All you need to do is enter the height, and the calculator will instantly provide the velocity at impact. It’s quick, easy to use, and designed to give clear results without manual calculations.
You can start using it right away, or keep reading to understand the formula, see an example, and learn how each parameter works.
Understanding the Formula
Height to Velocity Formula (for a falling object)
Velocity = √(2 × g × Height)
Variables:
- Velocity: The final speed of the object as it reaches the ground.
- g: The acceleration due to gravity (9.8 m/s² or 32.2 ft/s²).
- Height: The vertical distance from which the object is dropped.
In simple terms, the higher the drop height, the faster the object will be moving when it hits the ground. Gravity provides constant acceleration, which is why the formula includes the factor g.
Parameters Explained
Height
The initial vertical distance from which the object falls. It can be measured in meters or feet, depending on the unit system you are using. Greater height means more time to accelerate, leading to higher velocity.
g (Acceleration due to gravity)
A constant value that represents how quickly objects speed up when falling freely. On Earth, it’s approximately 9.8 m/s², but if you’re studying motion on another planet, this value will be different.
Velocity
The final speed of the falling object at ground impact. It is calculated using the above formula and expressed in meters per second (m/s) or feet per second (ft/s).
How to Use the Height to Velocity Calculator — Step-by-Step Example
Let’s go through an example calculation.
- Suppose an object is dropped from a height of 20 meters.
- Use the standard value for gravity, g = 9.8 m/s².
- Apply the formula:
Velocity = √(2 × g × Height)
Velocity = √(2 × 9.8 × 20)
Velocity = √392
Velocity ≈ 19.8 m/s
The final result is about 19.8 m/s, meaning the object would be traveling at nearly 20 meters per second when it hits the ground.
Additional Information
Here’s a quick reference table for different heights (using g = 9.8 m/s²):
| Height (m) | Velocity (m/s) |
|---|---|
| 5 | 9.9 |
| 10 | 14.0 |
| 20 | 19.8 |
| 50 | 31.3 |
This shows how velocity increases with greater height due to the constant pull of gravity.
FAQs
It calculates the final speed of an object falling freely from a certain height, assuming no air resistance.
Yes, if you’re calculating velocity on Mars, the Moon, or elsewhere, replace Earth’s gravity (9.8 m/s²) with the local value.
No, the calculation assumes free fall in a vacuum. Real-life objects falling through the atmosphere will experience slower velocities due to air resistance.