Calculate Uplift

Calculator for the uplift of a helium-filled balloon or other things lighter than air. The mass is the total mass of the device which should take off. Air density at normal conditions is about 1.2 kilograms per cubic meter. The higher you go, the less dense the air becomes. At 5500 meters it is half as high, but only very special balloons can reach this height. If helium is used as a lifting gas, then this has at equal conditions a density of 0.18 kilograms per cubic meter.

The calculation is done assuming that the volume of the weight is negligible compared to the volume of the balloon.

As a result, you'll get the volume, where the device is as heavy as air. To lift off, it must be larger. The balloon diameter is the minimum diameter of the spherical balloon.

The formulas for calculating the volume and diameter of the balloon are:
volume = mass / ( air density - lifting gas density )
balloon diameter = 2 * ³√ 3/4 * volume / π

Example: a person weighs about 80 kilograms. With clothing, equipment and the balloon, it is 100 kilograms. Then you need a volume of at least 98 cubic meters to take off, the round helium balloon would have a diameter of more than 5.72 meters.

Hot air is used more frequently than helium as a buoyant in hot air balloons. The air in such a balloon is heated to about 100 degrees, the density of the buoyant gas then drops to about 0.9, which is still much higher than that of helium. The volume required would be at least 333 cubic meters, the hot air balloon would need a diameter of over 8.6 meters. The diameter increases much less than the volume, as it is calculated as the cube root of the latter.