What is the best way to share variables between a large number of classes?

I'm using Java to do some complicated calculations, and have a lot of classes that need access to a lot of the same variables. These variables are set at different stages of the calculations, in different classes. The problem is that my code is getting quite messy as I am being forced to pass the same parameters to a lot of different methods.

I am looking for peoples thoughts on what the best approach here would be? One idea I have is to make a superclass with all these variables set in it and extend this class everywhere it is needed.

Another option is to pass an object holding all this information around from method to method but this seems overly complex. Neither of these solutions feel like the cleanest approach to me. Any thoughts or suggestions of design patterns/ideas that may help me are appreciated. Thanks for your help.