Here's how I figure it out if I'm using regular 40-42" fabric. My quilt is 54x72 so I should have a backing at least 3-4" wider on each side to grab on to when quilting so that makes it at least 60 x 80. So take fabric that's 42" wide plus I want my seam to go horizontal and not vertical as the seam would make a bulge as I advance the quilt. So the 1st piece I cut at 60" so basically 1.5 yds and I'll need another one the same size pretty much so that equals 3yds with not much if any length extra as you need to take in consideration of seams. I make my seam 1/2" instead of 1/4" to make sure it doesn't come loose. I press the seam open also.
Most times I'll buy backing fabric and then keep the leftover for yardage for another quilt so it's a win-win situation for me. Plus if you look at the prices of backing. You're getting 3yds for the price of 1 yard as most times its 108" wide so 2 yards of backing fabric will do the trick and gives you a lot of yardage left over for another quilt.