Pressure as a function of altitude above 11 km I need to calculate the force that causes a weather balloon with a specific volume to rise. Having searched for quite a few hours, I found the needed formula that can be used to calculate the pressure at a certain altitude. (surprisingly, the formula given on the German Wikipedia gives better values than that from the English one )

This is needed to get the density of the air, which can then be used with Archimedes' principle to get the buoyancy force of the balloon a that height.

However, it is stated that the formula only returns valid values for altitudes up to 11 km. Is there a way to calculate the air pressure at a higher altitude?
Those formulas are based on an assumption that the pressure is hydrostatic and the ideal gas law. The example given is limited to 11km but uses the tables from the U.S. Standard Atmosphere which actually go up to $1000$ km. Starting at Page 58 one can find values for pressure density and temperature above 11km.