Grip size with the conventional putter is much larger than the grip size for irons and woods.  The following video will show the effect of different grip sizes on your hip line as a result of tension and relaxation in your core.

If you use a belly or long putter, your grip sizes are different. However, improper left or right hand grip size with your putter will have the same effect on your hip line, COF and putter path. If you do the online measurements for your putter, you will be given left and right hand grip sizes for conventional, belly and long putters.