Yards of Material

How We Calculate

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How we calculate is simple to state: every result is geometry plus sourced data plus your inputs, done by tested code. This page shows the formulas, where the data comes from and where the results stop being reliable.

The core formula

Most calculators on this site answer “how much material covers this area at this depth?”

  1. Area. Rectangle: length × width. Circle: π × (diameter ÷ 2)². Ring, for rock or mulch around a tree: π × (outer radius² − inner radius²). Triangle from three measured sides: Heron’s formula. L-shape: two rectangles added together. You can also type a known area.
  2. Volume = area × depth. Inches are divided by 12 to get feet.
  3. Cubic yards = cubic feet ÷ 27, because a cubic yard is 3 ft × 3 ft × 3 ft.
  4. Extra. We add your waste allowance, and for materials that settle or compact we add a compaction allowance. The two multiply: volume × (1 + compaction) × (1 + waste).
  5. What to order. Bulk orders round up to the next half cubic yard, because that’s how most yards sell. Bags round up to whole bags.
  6. Weight = volume × the material’s density. Density changes with moisture and grading, so weight is shown as a range when our sources give one.

Unit conversions use exact definitions: 1 inch = 2.54 cm, 1 pound = 0.45359237 kg, 1 acre = 43,560 sq ft, 1 US ton = 2,000 lb.

Concrete, blocks, asphalt and firewood

  • Concrete slabs and footings: length × width × thickness. Columns and Sonotubes: π × radius² × height × count. Steps: each step is a solid block one run deep and as tall as all the steps up to it, plus an optional top landing. Fence posts: the hole’s volume above the gravel base, minus the post.
  • Bagged concrete: volume ÷ the manufacturer’s stated yield per bag, rounded up to whole bags.
  • Concrete blocks: wall area ÷ the block’s face area including the mortar joint (an 8 × 16 in face gives 1.125 blocks per sq ft), minus openings, plus your waste allowance.
  • Asphalt: area × compacted thickness × compacted asphalt density, in tons.
  • Firewood: a cord is 128 cubic feet of wood stacked tight, the legal definition in NIST Handbook 130. A face cord is one 4 × 8 ft face of a stack, as deep as the pieces are long. With 16-inch pieces that’s one third of a cord.

Where the data comes from

Every density, bag size, yield and recommended depth has a source and the date we checked it, and the material data table lists them all. We prefer, in order:

  1. US government publications: NIST, the USDA Forest Service and Forest Products Laboratory, USDA NRCS, FHWA and state transportation departments.
  2. Standards bodies and trade associations, such as the American Concrete Institute, the Portland Cement Association and the Interlocking Concrete Pavement Institute.
  3. Manufacturers’ data sheets for bagged products.
  4. University extension services.
  5. Published supplier, quarry and retailer data: a quarry’s own weight per yard, a retailer’s listed bag size, a truck maker’s spec sheet. We use these where no source above covers the material, and the data review flags each one.

We use Engineering ToolBox only as a fallback where nothing else gives a figure, and mark it as low confidence. We don’t use other calculator websites as sources. When sources disagree we keep both and show the range. If a value can’t be sourced well, the feature waits instead of guessing.

Moving it yourself

Calculators that sell bulk material also show how many trips it takes. Wheelbarrow loads = volume ÷ the wheelbarrow’s capacity filled level (6 cu ft, a common contractor model). Pickup trips are limited by whichever runs out first: the bed’s volume or the truck’s payload. We plan for the heavy end of the material’s weight range so no trip overloads the truck. The example truck is a 2026 Ram 1500 Tradesman with the 6′4″ box (61.5 cu ft, 2,360 lb payload, from Ram); you can enter your own payload from the sticker in the driver’s door jamb.

Prices

We never make up prices. Cost guides show national typical ranges built from published sources:

  1. Government data: Bureau of Labor Statistics wages and producer price indexes, and state transportation department bid prices.
  2. Prices that suppliers, quarries and ready-mix plants publish on their own websites.
  3. National cost guides that publish installed prices, with the year their figures are for.

For each item we pool every figure the sources give (a range counts both ends) and show the middle half of them, the 25th to 75th percentile, as the typical range. With fewer than four figures we show the full span instead. Figures we judge low-confidence are kept in our research files but never used. Every cost page lists its sources and the date we last reviewed the prices.

We round what we show, because pooled ranges aren’t accurate to the cent. Rates under $20 are rounded to the nearest 25 cents (5 cents under $1), and larger rates to the dollar. Totals for a job, an order or a delivery are rounded to the nearest $5, or $10 from $1,000. A single product’s shelf price, such as a bag of concrete, is shown as listed. Totals are worked out from the unrounded figures, so a total can differ slightly from a rounded rate multiplied by the area.

Prices vary a lot by region and season, so a typical range is a starting point, not a quote. The quote checker in each cost calculator turns a quote you received into a price per square foot (or per foot, or per yard) and shows where it falls against the typical range and against the full span of sources. A do-it-yourself estimate prices the materials alone, using the same volumes the calculators compute.

What the results can’t tell you

  • Moisture. Wet sand, soil and mulch weigh noticeably more than dry. Ask your supplier whether they sell by weight or volume.
  • Your supplier’s product. Gradings differ between quarries. If your supplier publishes a weight per yard, use theirs.
  • Ground conditions. Uneven subgrade, soft spots and how hard you compact all change what you use. That’s what the waste allowance is for.
  • Codes and safety. Slab thickness, footing depth and retaining-wall design can be set by local code. Call 811 before you dig.

Testing and corrections

The calculation code is checked by automated tests. The worked examples and the tables of common sizes and costs on our pages are generated by that same code from the same data. We check figures written into the text against the code and the data before a page is published, and again whenever the data changes. If you spot an error, the contact page tells you how to reach us. We fix it and update the page’s date.