Topsoil for New Lawns
A new lawn needs 4-6 inches of quality screened topsoil to give grass roots a proper growing medium. If you're sodding, the topsoil goes down first, is graded and compacted lightly, then sod is laid directly on top. If you're seeding, the topsoil is graded, lightly raked, seeded, and covered with a thin layer of straw mulch.
For a 2,000 sq ft lawn at 4 inches of topsoil: 667 cubic feet = about 25 cubic yards = about 27.5 tons. That's 4-5 dump truck loads. This is a significant material cost ($25-40/yard = $625-1,000) but it's the foundation that determines whether your lawn thrives or struggles.
Don't skip the grading step. Topsoil should be graded to slope away from the house (1-2% grade) for drainage. Low spots that pool water will kill grass and create mosquito habitat. Rent a landscape rake attachment or use a tractor-mounted box blade for large areas.