The volume formula, and why topsoil is priced by the cubic yard
Bulk topsoil suppliers sell by the cubic yard, so the first step is area times depth. For a rectangular bed or lawn section, that's length times width times fill depth, all converted to the same unit, usually feet. For a round bed or tree ring, swap the rectangle for a circle: pi times the radius squared, times depth. Either way, the result comes out in cubic feet. A cubic yard holds 27 cubic feet, so the last step is dividing by 27, which lands on the unit a supplier's price sheet is actually written in.
Bagged topsoil is priced differently: by the bag, at a fixed cubic-foot size per bag. Scotts Premium Topsoil, sold at Home Depot, Lowe's, and Amazon, ships in 0.75 cubic foot bags, but sizes vary by brand from roughly 0.5 to 2 cubic feet, so this calculator lets you pick the bag size on the label rather than assuming one universal number.
A new lawn and a raised bed: the math behind both
A 1,200 sq ft yard getting fresh topsoil worked into the top 4 inches, the till depth the University of Maryland Extension's lawn-establishment guide recommends for blending amendments into existing soil: volume = 1,200 x (4/12) = 400 cu ft, which is 14.81 cu yd. Using the loam density preset (87.2 lb/ft³), that's 34,880 lb, or 17.44 tons, before any settling allowance. Add a 10% allowance for the soil compacting once it's spread and watered in: 400 x 1.10 = 440 cu ft, 16.30 cu yd, 38,368 lb (19.18 tons).
A 4 ft by 8 ft raised bed on a patio, filled to the 8 in minimum the University of Maryland Extension gives for growing leafy greens, beans, or cucumbers in a bed sitting on a hard surface: volume = 32 x (8/12) = 21.33 cu ft, or 0.79 cu yd. At the loam density, that's 1,860 lb (0.93 tons), and at 0.75 cu ft per bag, 29 bags before settling, 32 bags with a 10% allowance. For a bed shallower than 16 inches, the same Extension guidance caps straight topsoil at 20% of the mix by volume, so most of that fill would come from compost and a soilless growing medium rather than topsoil alone.
Why the weight estimate depends on soil texture, not just volume
A cubic yard of topsoil doesn't have one fixed weight, because bulk density (mass per unit volume) changes with how much sand, silt, clay, and organic matter the soil contains, plus how wet it is when it's weighed. Rather than pick one number and call it universal, this calculator's three texture presets come from the USDA NRCS Soil Health Educators Guide (2023), which publishes an ideal bulk-density ceiling for each texture group, the density a soil should stay at or under for roots to grow through it freely. Converted to pounds per cubic yard: sand and loamy sand top out around 2,692 lb, sandy loam through silt loam around 2,354 lb, and clay-heavy textures around 1,850 lb.
That NRCS table describes undisturbed or tilled soil in the ground, not necessarily loose, screened topsoil sitting in a supplier's stockpile, which tends to stay looser, and lighter per cubic yard, until it settles. Moisture matters too: wet soil can weigh noticeably more than the same soil dry, sometimes enough to swamp the difference between texture presets. Treat the preset as a planning estimate, and if a supplier gives you a lab-tested or load-ticket density, enter it directly with the custom option instead.
There's a second number in that same NRCS table worth knowing, because it answers a different question than the ideal ceiling this calculator uses. The ideal figures above describe soil light enough for roots to grow through freely; they are not the point where a soil actually becomes a problem. That same source also publishes a higher bulk-density threshold, the point past which root growth is measurably restricted: about 112 lb/ft³ for sandy soils, roughly 103 to 112 lb/ft³ across the loam-family textures this calculator groups together, and about 92 to 98 lb/ft³ for the clay-heavy end. A stockpile or a freshly delivered load sitting above the calculator's texture preset isn't automatically a problem; loose topsoil settles as it's watered and walked on, and some settling toward the ideal ceiling is expected and even accounted for by this calculator's settling allowance. What's worth watching for is soil that keeps compacting well past that ceiling and toward the restrictive threshold, which SDSU Extension attributes mainly to heavy equipment traveling over wet ground; working organic matter into compacted soil is one of the practices the same source lists for bringing bulk density back down.