It is of paramount importance to know in advance how much the moving company will charge you for the moving job. Cost estimates over the phone or email are non-binding and almost always end up being inaccurate. This is why it is strongly recommended that you request an in-house written estimate from your selected mover. These written estimates are much more precise and can guarantee to some extent the final price of the relocation. And, if possible, try to obtain such on-site estimates by at least three moving companies so that you can compare the moving rates.
Here is an explanatory video about the types of moving estimates and quotes: