Methodology & Sources

How we calculate

All YardMath calculators use the same core volume formula: area (sq ft) × depth (ft) ÷ 27 = cubic yards. Then material-specific constants convert volume to weight or unit counts. This page documents every constant used, its source, and our assumptions.

Volume formula

Cubic feet   = area (sq ft) × depth (ft)
Cubic yards  = cubic feet ÷ 27
Cubic meters = cubic feet × 0.0283168

For circles: area = π × (diameter/2)². For triangles: area = 0.5 × base × height. All measurements are converted to feet before multiplying.

Waste and compaction factors

We apply a default waste factor to account for:

Gravel/crushed stone: 10% default. Compactable gravel (crusher run, #21A) compacts roughly 10–15%, so we recommend 15% for those materials.
Mulch: 5% default. Mulch does not compact significantly but beds often have irregular edges.
Topsoil: 10–15% default. Loose topsoil settles 10–20% after watering over the first season.
Concrete: 10% default. Bags mixed manually rarely achieve exactly the published yield; pour waste adds to this.
Pavers: 10% default for running bond, 15% for herringbone 45°. Pattern waste is primarily from edge cuts.

Material densities (lb per cubic yard)

Densities assume dry, loose material. Wet material can weigh 5–15% more. Source: Braen Stone bulk material data; USGS Open-File Report 2006-1195.

Material	lb/yd³	Tons/yd	Source
Pea Gravel	2,700	1.35	Braen Stone
Crushed Stone #57	2,700	1.35	Braen Stone / USGS
Crushed Stone #411	2,875	1.44	Braen Stone
Crusher Run (#21A)	2,850	1.43	Braen Stone
River Rock	2,835	1.42	Braen Stone
Decomposed Granite	2,565	1.28	Braen Stone
Concrete/Mason Sand	2,700	1.35	USGS
Play Sand	2,430	1.22	USGS
Lava Rock	1,215	0.61	Braen Stone
Topsoil (screened)	2,025	1.01	ISU Extension average
Compost	1,000	0.50	Cornell Waste Mgmt Inst.
Shredded Wood Mulch	450	0.23	Penn State Extension
Bark Mulch	540	0.27	Penn State Extension
Rubber Mulch	675	0.34	Rubber Mulch Direct

Concrete bag yields

Based on Quikrete published product specifications. Sakrete and other brands have similar but not identical yields — always check the bag label.

Bag size	Yield (cu ft)	Bags per cu yd
40 lb	0.30	90
60 lb	0.45	60
80 lb	0.60	45

Source: Quikrete Concrete Mix product specification

Grass seed seeding rates

All rates are lb of pure live seed (PLS) per 1,000 sq ft. New seeding rates assume bare soil with good seedbed preparation. Overseeding rates are typically 50–60% of new rates.

Species	New (lb/1k sq ft)	Overseed	Source
Kentucky Bluegrass	2	1	University of Minnesota Extension
Tall Fescue	8	4	Purdue Extension
Fine Fescue	4	2	Penn State Extension
Perennial Ryegrass	8	4	Purdue Extension
Bermudagrass (hulled)	2	1	Clemson Extension
Zoysiagrass	2	1	NC State Extension
Centipedegrass	0.25	0.125	Clemson Extension
Bahiagrass	7	3.5	UF/IFAS Extension

Fertilizer calculation

lb of product = (area ÷ 1,000) × target lb N per 1,000 sq ft ÷ (N% ÷ 100). Default target rate is 1.0 lb N per 1,000 sq ft per application, based on Purdue Extension and Penn State Extension lawn fertilization guides. Annual total rates vary by species.

Paver base specifications

Gravel base depth (ICPI standard): 4 inches for pedestrian traffic, 6 inches for vehicular. Bedding sand: 1 inch, screened concrete sand. Polymeric sand coverage estimated from manufacturer data at 40–80 sq ft per 50 lb bag depending on paver size and joint width.

Source: ICPI Interlocking Concrete Pavement Institute installation guidelines

Rounding rules

Volume results round to 2 decimal places. Bag counts always round up (ceiling) — never short-order a project. Ton results round to 2 decimal places. When a result is 0 or NaN, we display "—" rather than a misleading number.

Limitations and disclaimers

Material densities are average values for dry, loose material delivered to site. Actual densities vary by moisture content, source quarry, and whether material has been compacted. Concrete bag yields assume proper water-to-cement ratio; over-watering reduces strength and yield. Always confirm quantities with your supplier before placing a final order. Structural applications (retaining walls, footings, deck framing) must comply with local building codes and may require engineering review.