Calculate velocity from height for a drop from rest with v = √(2gh), using Earth gravity or your own acceleration, or find the height for a given speed.
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Height to Velocity Formula
The following equation is used to calculate the velocity from height.
- Where V is the velocity (m/s)
- H is the height (m)
- a is the acceleration due to gravity (m/s^2)
For motion from rest with constant positive acceleration and no air resistance, multiply 2 by the vertical drop and acceleration, then take the square root. This gives the final speed magnitude.
| Height (m) | Velocity (m/s) |
|---|---|
| 0.10 | 1.401 |
| 0.25 | 2.215 |
| 0.50 | 3.132 |
| 0.75 | 3.836 |
| 1.00 | 4.429 |
| 1.50 | 5.425 |
| 2.00 | 6.264 |
| 3.00 | 7.672 |
| 4.00 | 8.859 |
| 5.00 | 9.905 |
| 7.50 | 12.131 |
| 10.00 | 14.007 |
| 12.00 | 15.344 |
| 15.00 | 17.155 |
| 20.00 | 19.809 |
| 25.00 | 22.147 |
| 30.00 | 24.261 |
| 40.00 | 28.014 |
| 50.00 | 31.321 |
| 100.00 | 44.294 |
| *Assumes free fall from rest, ignoring air resistance. Formula: v = √(2gh), with g = 9.81 m/s². | |
How to Calculate Velocity from Height?
Example Problem:
The following example outlines the steps and information needed to calculate Height to Velocity.
First, determine the height. In this example, the height is found to be 50 m.
Next, determine the acceleration due to gravity. This is known to be 9.81 m/s^2.
Finally, calculate the velocity from height using the formula above:
V = SQRT(2*a*H)
V = SQRT(2*9.81*50)
V ≈ 31.3209 m/s
