How We Calculate: Methodology and Sources

This page explains the formulas, definitions and sources behind every calculator on CubicYardCalcs.com, so you can check any number we give you.

Units and Definitions

All unit definitions follow the US National Institute of Standards and Technology. NIST Handbook 44, Appendix B states that the yard has been defined as exactly 0.9144 meter since 1959. NIST Handbook 44, Appendix C gives the tables we use:

Unit

Definition

1 cubic yard

27 cubic feet (exactly) = 46,656 cubic inches, about 0.765 cubic meters

1 cubic foot

1,728 cubic inches

1 short ton (US ton)

2,000 pounds (exactly)

1 metric ton (tonne)

1,000 kilograms = 2,204.623 pounds

1 long ton

2,240 pounds (exactly)

Volume Formulas

  • Rectangle: length × width × depth, all in feet, divided by 27 for cubic yards. Depth in inches is divided by 12 first.
  • Circle: 3.14159 × (diameter ÷ 2)² × depth, divided by 27.
  • Triangle: base × height ÷ 2 × depth, divided by 27.
  • Several areas: each area is calculated separately and the volumes are added.
  • Waste allowance: the total is multiplied by 1 plus the percentage you choose (for example × 1.10 for 10 percent).

Material Weights

Weights are shown as ranges because moisture, compaction, and source change the weight of the same material. Each range is converted to US short tons per cubic yard:

Unit

Tons per cubic yard

Source

Mulch, wood chips

0.12 to 0.24

US EPA, Volume-to-Weight Conversion Factors (April 2016): wood chips 243 lb (dry) to 473 lb (green) per cubic yard

Topsoil

1.02 to 1.69

Material weight chart sourced to EPA and NTEA, loose to wet [add link]

Fill dirt (clay)

1.15 to 1.49

Same chart, dry to wet

Gravel, 3/4 inch

1.28 to 1.69

Same chart, dry to wet

Crushed stone

1.35

Same chart, average

Sand

1.38 to 1.65

Same chart, dry to wet

Concrete, poured

1.82 to 2.16

ACI 318-14, clause 2.3: normal-weight concrete 135 to 160 lb per cubic foot

Asphalt

1.35

Material weight chart sourced from EPA and NTEA

Cross-check for soil: the USDA NRCS sheet Soil Quality Indicators: Bulk Density lists ideal bulk densities below 1.60, 1.40 and 1.10 g/cm³ for sandy, silty and clayey soils, roughly 1.35, 1.18 and 0.93 tons per cubic yard of dry soil, consistent with the dry end of our soil ranges.

What we do not use: the EPA conversion factors also list dirt and sand at 929 lb and concrete at 860 lb per cubic yard, but those rows describe loose construction and demolition debris for waste planning, not delivered material, so they are excluded from our calculators.

Depth Recommendations

Mulch and stone depths quoted on our pages come from university extension services: University of Minnesota Extension, Iowa State University Extension, Penn State Extension and University of Maryland Extension. Each page names the service it quotes and links to it.

Rounding

  • Cubic yards are shown to two decimal places; tons to one decimal place.
  • Suggested order sizes are rounded up to the next half cubic yard, because many suppliers load in half yard steps. Ask your supplier for theirs.
  • Bag counts are always rounded up, since stores do not sell part of a bag.

Testing, Updates and Corrections

Every calculator is tested against hand-worked examples before it is published, and the worked examples on each page match the tool’s default inputs so you can check them yourself. We review sources when they are updated. If you find an error, email [[email protected]] and we will correct confirmed mistakes and update the review date above.