Calculate vertical drop, constant acceleration magnitude, or final speed for ideal motion from rest with no air resistance, using selectable units.

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Starts from rest with constant positive acceleration and no air resistance. Velocity is reported as speed.

Default 9.81 m/s² is an approximate Earth-gravity value.

Height to Velocity Formula

The following equation is used to calculate the velocity from height.

V = SQRT(2 × a × H)
  • 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 to Velocity Conversion Table (Free fall, g = 9.81 m/s²)
Height (m) Velocity (m/s)
0.101.401
0.252.215
0.503.132
0.753.836
1.004.429
1.505.425
2.006.264
3.007.672
4.008.859
5.009.905
7.5012.131
10.0014.007
12.0015.344
15.0017.155
20.0019.809
25.0022.147
30.0024.261
40.0028.014
50.0031.321
100.0044.294
*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 50m.

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