Buoyancy in gases:

How can one calculate the magnitude of the lifting force?

According to the Archimedean Priciple the buoyancy a body is affected by equals the weight force of the displaced gas:

The weight force is the product of the mass and the gravitational constant:

You already know the mass. It is the product of density and volume:

Thereby, ρ is the density of the displaced gas.
is the volume of the body, which is within the gas.

Thus one can calculate the magnitude of the lifting force, which is acting on a body in a gas, according to the Archimedeam Priciple.