How much fill dirt you need
Measure the hole or the low spot, multiply length × width × depth in feet, and divide by 27 for cubic yards. A dip 10 feet by 20 feet that needs 6 inches of fill is 10 × 20 × 6/12 = 100 cubic feet, or 3.70 cubic yards. Fill is sold loose by the yard, so the page rounds the order up to the next quarter yard: 3.75 yd³.
Measure the depth where the fill will be, not at the deepest point: a dip that slopes from nothing at the edge to 6 inches in the middle holds less than a box 6 inches deep. Split it into areas at their own depths, or measure an average depth, and the page adds the areas up.
What a yard of fill weighs
The weight is for the truck, not the order. The page uses the Natural Resources Conservation Service's figure for loam: a bulk density under 1.40 g/cm³ is ideal, about 2,360 lb a cubic yard, measured dry in the ground. At that weight the 3.70 yards above come to 8,741 lb, which is 4.37 short tons (2,000 lb each), or 3.96 tonnes (1,000 kg each).
Fill is whatever the supplier dug, so its weight moves with what it is made of. The same NRCS guide puts the ideal for sand under about 2,697 lb a yard, 1.35 short tons (2,000 lb), and for clay under about 1,854 lb, 0.93 short tons. Moist soil weighs more than any of these. With fill dirt picked as the material, its weight is a box under Assumptions: type your supplier's figure and the weight and the loads follow it.
Hauling it yourself
A pickup is limited twice, by its bed and by its payload, and with dirt the payload wins. The 3.70 yards above fit in two beds of 2.27 yd³, but at 8,741 lb a pickup carrying about 1,500 lb needs 6 loads. Your truck's payload is on the sticker in the driver's door jamb; type it under Assumptions and the page counts with it, and says so if the load is over.
Settling, compaction and waste
Soil settles when it is watered. We found no source we would stand behind for how much, for dirt of unknown make-up, so the page adds nothing for it. If your supplier or your contractor gives you a figure, type it into the waste box: it is added once, to the yards, the weight and the order.
Topsoil to finish the surface is its own question — sold by the bag as well as by the yard — and the link under the answer carries this area to the topsoil page. We are not connected with any supplier or store.