How We Calculate

The formulas, sources and assumptions behind every Terrainity calculator.

Updated September 27, 2026

Volume: the base of almost everything

Most materials are ordered by volume, so most calculators start the same way:

Area (sq ft)×Depth (in) ÷ 12=Cubic feet÷27=Cubic yards

Areas come from length × width, or from the shape formulas in the square footage calculator (circles, triangles by Heron's formula, trapezoids, ovals). Land uses 43,560 square feet per acre and the international foot (0.3048 m).

Weight: from cubic yards to tons

Stone, sand and soil are usually sold by the ton, so we multiply cubic yards by a weight per yard. We use the middle of a published range and show it in the result, so you can replace it with your supplier's figure:

MaterialWeight usedSource range
Crushed stone1.4 t/yd³1.35–1.7 t (Stone Center)
Pea gravel1.5 t/yd³1.4–1.6 t (Stone Center)
River rock1.5 t/yd³1.4–1.75 t (Stone Center)
Landscape gravel1.3 t/yd³1.25–1.35 t (Stone Center)
Dry sand1.35 t/yd³2,700 lb/yd³ (The Calculator Site)
Topsoil, fill dirt1.2 t/yd³1–1.35 t depending on moisture

Waste and compaction allowances

Where material is cut (sod, pavers, boards) or compacted (bases, fill), the calculator adds an allowance. When no published figure applies, we say it's our default and let you change it. Suppliers know how their own material behaves, so their number beats ours.

Standards and references we follow

  • Pavers: ICPI Tech Spec 2 for base thickness (4 in pedestrian, 6 in driveways), 1 in bedding sand and joint widths.
  • Decks: American Wood Council DCA 6 for board spacing and fasteners.
  • Fence posts: QUIKRETE's method for hole width and depth.
  • Playground surfacing: CPSC Public Playground Safety Handbook.
  • Lawns and soil: Penn State, University of Maryland, Oregon State and UC extension publications.

Rounding

Bags, pallets, boards and posts are rounded up to whole units, because you can't buy part of one. Tons and yards are shown to two decimals so you can round to your supplier's minimum.

The PDF report

The “Download PDF report” button creates the PDF in your browser. It contains only the estimate: your measurements, the result, the shopping list, key figures and the calculation steps, with the project name you type. Nothing is sent to our servers.