Bank yards, loose yards and swell
Excavation volume starts as simple geometry: length × width × depth in feet, divided by 27 to get cubic yards. That figure is the bank yardage — the soil as it sits compacted in the ground. The moment a bucket lifts it, the soil breaks apart and takes up more room. That expansion is called swell, and for ordinary topsoil and clay loam it runs around 25%, so 10 bank yards fills roughly 12.5 yards of truck bed. Rock, hardpan and wet clay swell more; clean sand swells less. This calculator sizes the trucks and the hauling bill on the loose (loaded) volume, because that is what actually fills the box, and estimates weight at about 1.1 tons per loose cubic yard.
Two practical points before you book a machine. First, a dumpster has a weight cap as well as a volume cap, and soil is heavy enough that you will usually hit the weight limit long before the box looks full — ask your hauler for the tonnage allowance and split the dirt across more loads if needed. Second, the walls of a dig rarely stay vertical: if you are benching or sloping the sides for safety, or over-digging for footing forms and backfill room, your real volume can be noticeably larger than the nominal hole, so measure the top of the cut, not the bottom.
Before any digging, call 811 in the US (or your local one-call service) to have buried utilities located and marked. It is free, it is usually required by law, and hitting a gas, power or fibre line is the single most expensive mistake on a small excavation job.
Swell, soil weight and haul rates vary a lot with soil type, moisture, access and disposal site distance. Treat this as a planning estimate and confirm with your excavator or hauler.