Cubic Yards Calculator

How to calculate cubic yards

Find the area in square feet, multiply it by the depth in inches, then divide by 324. The 324 is 27 cubic feet in a cubic yard times 12 inches in a foot. For a 10 × 10 ft area 4 inches deep, 100 × 4 ÷ 324 = 1.23 cubic yards. Clemson Cooperative Extension's mulch fact sheet puts it this way: "One cubic yard will cover a 324-square-foot area with an inch of mulch."

Only the area changes with the shape. A circle is π times the radius squared, where the radius is half the distance across. A circle 10 ft across covers 78.54 sq ft. A triangle is half the base times the height, measured square to the base. A ring is the outer circle minus the hole: 12 ft across with an 8 ft hole leaves 62.83 sq ft. For an L-shaped bed, add two rectangles: 10 × 10 ft plus 6 × 4 ft is 124 sq ft, or 1.53 cubic yards at 4 inches.

Gravel, sand and soil can be sold by weight as well as by volume, so you need the tons too. Multiply the amount to order by the material's weight per loose cubic yard, then divide by 2,000 lb, the short ton. The sections below give the weights and the reasons to order more than you measure.

Cubic yards formula

rectangle area = L × W
triangle area = ½ × B × H
circle area = π × (D ÷ 2)²
ring area = π × ((Do ÷ 2)² − (Di ÷ 2)²)
cu ft = area × depth ÷ 12
cu yd = area × depth ÷ 324
m³ = cu yd × 0.764554857984
order = cu yd × 1.10 (concrete under 200 cu yd; 1.05 from 200)
order = cu yd × 1.17 (gravel or sand) or × 1.39 (soil), when compacted
tons = order × lb per loose cu yd ÷ 2,000
order is worked from cu yd, and tons from order, each rounded to 2 decimals first (unrounded when it would show as less than 0.01)
L length · W width · B base · H height · D diameter
Do outer and Di inner diameter, all in ft · depth in inches

Worked examples

A gravel pad 10 × 10 ft and 4 inches thick, compacted, holds 1.23 cubic yards in place. Times 1.17 gives 1.44 loose cubic yards to order. At 2,850 lb a loose cubic yard that is 4,104 lb, or 2.05 tons.

A round concrete patio 12 ft across and 4 inches thick covers π × 6² = 113.10 sq ft and holds 1.40 cubic yards. With 10% extra the order is 1.54 cubic yards, or 1.75 if the plant sells quarter yards. The order weighs about 3.12 tons.

A military estimating manual (TM 3-34.41, 2021) prints a table of concrete per 100 sq ft. This calculator gives the same 1.85, 2.47 and 3.70 cubic yards for its 6, 8 and 12 inch rows. Its 4-inch row says 1.24 and its 10-inch row 3.90, but its own cubic feet give 33.3 ÷ 27 = 1.23 and 83.3 ÷ 27 = 3.09.

Assumptions and limits

• The depth is the same across the whole area. For uneven ground, enter the average of several measurements.
• Areas are measured flat, as seen from above. On a slope, see the special cases above.
• The weights of gravel, sand and soil are the Army's averages for common materials. Your supplier's own figures come first. With Other, the calculator uses your density and, when compacted, the factor for sand and gravel.
• Concrete includes the waste allowance explained under ordering. Mulch is worked by volume only.
• Sizes from 0.01 to 10,000 ft and depths from 0.01 to 1,200 inches.
• Slab thickness and base depth come from your plans or local code.

These figures are calculation aids, not a code determination. Always follow the code adopted where you live, your local inspector and a licensed professional. Terms of use.

Before you order

Ask the supplier for its weight per loose cubic yard, then choose Other and enter it in tons per cubic yard: divide pounds by 2,000, so 2,850 lb is 1.425. Across the Army's range for dry gravel, the default order could weigh 1.94 to 2.16 tons. Compare per-ton and per-yard prices with the aggregate price comparison calculator.

Check the delivery ticket against the amount to order: 1.44 loose cubic yards for the default base. If you order by weight without the supplier's figure, 2.16 tons covers that even at 3,000 lb a yard, the heavy end for dry gravel; at the light end it is 1.60 loose cubic yards.

Before you haul it yourself, compare the weight with the tire and loading placard on the driver's door pillar or, on some trucks, a door edge. Federal Motor Vehicle Safety Standard No. 110 (49 CFR 571.110, S4.3) puts one on trucks rated 10,000 lb GVWR or less, except incomplete vehicles, and has it say "The combined weight of occupants and cargo should never exceed XXX kilograms or XXX pounds." The default order weighs 4,104 lb. The payload capacity calculator does the subtraction, and the dump truck load calculator counts loads for bigger jobs.

With 10% extra, the 10 × 10 ft area 4 inches thick takes 61 bags of 80 lb concrete mix. As mulch it takes 17 bags of 2 cubic feet. The concrete bags calculator and the mulch calculator handle other bag sizes.

Frequently asked questions