Why is Illustrator adding whitespace around my artboard?

I'm struggling for a while with the whitespace Illustrator is creating around my prints.

For example I've set the artboard to be this size:

But when I've saved my print as an eps it is always this big:

I know there is an option to save as web and then to uncheck 'Clip to artboard' but I really need to save it as an EPS.

Can someone explain this to me please?