Methodology — Formulas and Density Table

Volume formulas

All volumes reduce to Euclidean geometry converted at 27 cubic feet per cubic yard. The formulas, in plain text exactly as the tool applies them:

• Rectangle / square: cu ft = L(ft) × W(ft) × D(ft), then cu yd = cu ft ÷ 27
• Circle: cu ft = π × radius(ft)² × D(ft), with π ≈ 3.14159 and radius = diameter ÷ 2
• Border / ring: cu ft = (OL × OW − (OL − 2×bw)(OW − 2×bw)) × D(ft), where OL/OW are outer length/width and bw is border width; inner terms are clamped at zero

Depth entered in inches or centimeters is converted to feet first (in ÷ 12; cm ÷ 30.48). Metric dimensions (m + cm) convert at 1 m = 3.28084 ft. The waste toggle multiplies volume by 1.05 or 1.10 — the widely recommended 5–10% allowance for compaction and settling.

Weight: the density table

tons = cubic yards × density, where density is short tons (2,000 lb) per cubic yard for the selected material. The table the calculator uses, with the reasoning per row:

These are industry-typical planning values, not constants. They agree with common reference ranges — for example, the Engineering ToolBox's solids-density table (engineeringtoolbox.com) lists crushed stone at about 100 lb per cubic foot, which is 2,700 lb (1.35 short tons) per cubic yard, inside our 1.35–1.6 band for dense gravels. Real loads vary with gradation, parent rock, and moisture. Stone grade names and sieve bands follow the AASHTO M 43 / ASTM D448 aggregate designation systems used by US quarries.

Bags, cost and rounding

bags = cubic feet ÷ 0.5, because bagged gravel in US retail is predominantly 0.5-cubic-foot bags (the typical 50 lb bag of #57); results round up to whole bags since nobody sells 0.4 of a bag. cost = tons × $/ton or cu yd × $/yd³ depending on the quote style — the two modes exist because suppliers quote both ways, and the density table is what makes them interchangeable.

Display rounding: cubic feet to 1 decimal, cubic yards and tons to 2, cubic meters to 2, cost to 2. Storage rounding: shared links and localStorage keep 2-decimal inputs, ample for site-measured precision.

Sourcing and review practice

Formulas are public-domain geometry; density and price figures are labeled typical values, reviewed against published references and supplier practice, and dated below. We prefer named, checkable sources over vibes: AASHTO M 43 / ASTM D448 for grade designations, Engineering ToolBox for the crushed-stone weight cross-check, and published national cost ranges (such as HomeGuide's gravel cost guides) for price bands — always presented as ranges, never point claims. When we cannot verify a figure to that standard, we hedge rather than invent precision.

Spot-check us: a 12 × 12 ft patio at 3 inches should return 36 cu ft, 1.33 cu yd, 1.87 tons of #57, 72 bags — the calculator's defaults on the homepage are pre-set to exactly that case.