Calculate Maximum Height from Upward Velocity

Calculator for the height an item can reach, which is moving up with a certain speed. The air resistance is neglected here, this can be done for compact bodies and speeds that appear e.g. at throwing. The item has a start velocity vertically up and then isn't accelerated anymore. The gravitational force lets it reach a certain height and then fall back down again.
Enter one value at velocity and height, the other value will be calculated.

Velocity (v):		m/skm/hmph
Height (h):		metersyardsfeet
g-acceleration (g):		m/s²

Round to 0 1 2 3 4 5 decimal places.

Example: a ball, thrown vertically up with a speed of 25 kilometers per hour, can reach a maximum height of almost 2.46 meters above its starting point. At 50 km/h it is about 9.83 meters.

The formula for calculating the theoretical maximum achievable height is h=v²/(2g).

So you need high speeds to actually reach more than a few meters in height. At high speeds, however, air resistance does play a role and reduces the actual achievable height. Air resistance depends on the shape and mass of the moving object, as well as on the quality of the air. For very high speeds and the associated heights, the air gets thinner the higher you go, and air resistance decreases accordingly. A calculation that takes air resistance into account is therefore very complicated. However, you can assume that objects that are supposed to move upwards at high speeds are designed to have as little air resistance as possible. This calculator then produces a value that is not achievable, but which serves as the upper limit for the maximum height.

Last updated on 05/21/2025. Author: Jürgen Kummer


German: g-Beschleunigung