Topsoil is heavy. A single cubic yard weighs roughly a ton dry and can pass 3,000 pounds after rain, so the number that usually decides your order is not the volume — it is whether the truck can reach the spot and whether you can move it once it lands.
How much depth do you actually need?
For top-dressing an existing lawn, one to two inches is plenty. Any more and you bury the grass.
For a new lawn, four inches of good soil gives roots room to establish. For garden beds, six inches. For raised beds where nothing grows below, go the full depth of the box — usually eight to twelve inches.
Raised beds are where people under-order most often. A 4 by 8 foot bed filled 10 inches deep needs almost exactly one cubic yard, which surprises anyone who assumed a few bags would do it.
Topsoil, garden soil and fill dirt are different things
Fill dirt is subsoil. It is cheap, it compacts well, and almost nothing grows in it. Use it to raise a grade, not to plant in.
Screened topsoil has been passed through a mesh to remove rocks and root chunks. It is what you want under sod or in a bed.
Garden soil or a soil blend is topsoil already mixed with compost. It costs more per yard, but if you were going to buy compost separately, the blend is often the better deal.
Settling
Loose delivered soil settles. A bed filled level to the rim in spring will sit an inch or two low by midsummer, and more if there is organic matter in the mix.
Order about 10 percent over your calculated volume and mound it slightly. The waste factor field above does this for you.
Delivery and hauling
Most suppliers charge a flat delivery fee regardless of quantity, so ordering three yards in one drop costs much less than three separate one-yard trips.
If you are hauling it yourself, remember the weight. One cubic yard of moist topsoil is about 2,200 pounds — at or past the legal payload of many half-ton pickups.