Do you have access to an ammeter? If you want a good idea how much current YOUR project is drawing, go down to Harbor Freight Tools and buy a $5 multimeter.
Well you need two pieces of information to estimate or calculate the duration from the battery. First is the mAH rating specification of your battery cell and second the current consumption drawn by your arduino. You do this second reading using your meter in it's current reading function (in series) not by reading the battery voltage with the meters voltage reading function.Lefty