How to Figure Cubic Yards for Concrete, Mulch and Gravel
Why this matters
Bulk material is sold by the cubic yard, measured on site in feet and inches, and the conversion between the two is where orders go wrong by a factor of three or twelve. A concrete truck that arrives a yard short leaves a cold joint in a slab or a crew waiting on a second, smaller load. A mulch order three times too big lands in the customer's driveway and has to be hauled away. The arithmetic is one line. This card is that line, the order to do it in, and the coverage check that catches a bad answer before the supplier's dispatcher does.
The formula, and where the 27 comes from
Cubic yards = length (ft) x width (ft) x depth (ft) / 27
A cubic yard is a cube 3 ft on each side: 3 ft x 3 ft x 3 ft = 27 cu ft. So once length, width and depth are all in feet, their product is in cubic feet, and dividing by 27 turns cubic feet into cubic yards.
The usual slip is dividing by 9 instead. Nine is the number of square feet in a square yard (3 x 3), which is an area conversion. Volume has three dimensions, so it needs 3 x 3 x 3. Dividing a volume by 9 gives an answer exactly three times too large. The trouble card on that exact error walks a real order through it; see related: The Mulch Order That Came Three Times Too Big.
The coverage line
This table is worth taping inside the estimating binder. It is the same formula run backwards: how many square feet one cubic yard covers at a given depth.
ONE CUBIC YARD = 27 CU FT = 324 SQ FT AT 1 IN DEEP
Depth Depth in ft Sq ft covered per cu yd
----- ----------- -----------------------
1 in 0.083 ft 324
2 in 0.167 ft 162
3 in 0.250 ft 108
4 in 0.333 ft 81
6 in 0.500 ft 54
Rule: sq ft / (324 / depth in inches) = cu yd
Where 324 comes from: 27 cu ft spread 1 in (1/12 ft) thick covers 27 / (1/12) = 27 x 12 = 324 sq ft. Every other row is 324 divided by the depth in inches. You can rebuild the table on a job with no notes, which is why it makes a good check.
The steps
1. Get the area in square feet. For a rectangle, length times width. For an L-shaped patio or a curved bed, break it into rectangles, triangles and circle pieces and add them; see related: How to Find the Area of an Irregular Room by Decomposition. A round pad uses the circle area; see related: Circles in the Field: Area, Circumference and the Diameter Trap. Keep the area unrounded.
Hazard at this step: if the job involves digging out a base or setting forms below grade, the area you are measuring is also the area you are about to excavate. Call your state's one-call locate service (811) and wait for the marks before anyone digs, and if a line is struck, stop, get everyone clear and call the utility.
2. Convert the depth to feet before you multiply. Depth is nearly always given in inches. Divide by 12 first: 4 in / 12 = 0.333 ft. Do this as its own written line. Multiplying feet by feet by inches gives a number in a unit nobody can order (square-foot-inches), and the shortcut of "divide by 27 and by 12 at the end" works only if you remember both divisions.
3. Multiply area by depth to get cubic feet. The unit on this line is cu ft, and you should write it.
4. Divide by 27. The unit is now cu yd.
5. Check against the coverage line. Divide the area by the coverage number for that depth. You should get the same answer as step 4. If you do not, one of the two is wrong, and finding which takes a minute.
6. Add the overage, then round up to what the supplier sells. Overage covers base that is lower than planned, spillage, forms that bow, and material that compacts. For ready-mix concrete, many contractors add something in the range of 5 to 10 percent, tuned to how true their subgrade usually is; see 'The Materials Waste Factor Worth Measuring' for setting your own figure. Then round up to the increment the plant or yard actually sells, which varies by supplier. Ask what it is and what their minimum load is; a small order below the minimum often carries a short-load charge, which is a reason to consider bagged material on a very small pour.
Worked example 1: a 10 by 10 ft slab, 4 in thick
Line Item Value Unit
1 Length 10.00 ft
2 Width 10.00 ft
3 Area = L1 x L2 100.00 sq ft
4 Depth 4 in
5 Depth / 12 0.333 ft
6 Volume = L3 x L5 33.33 cu ft
7 Cu yd = L6 / 27 1.23 cu yd
8 Check: L3 / 81 1.23 cu yd
The slab is 1.23 cu yd. The coverage check at 4 in (81 sq ft per yard) gives 100 / 81 = 1.23 cu yd, the same answer.
Overage. At 8 percent, 1.23 x 1.08 = 1.33 cu yd. If the plant sells in quarter yards, that rounds up to 1.5 cu yd. If it sells in half yards, also 1.5 cu yd.
The depth you assumed versus the depth you have. Before ordering, measure the depth from the top of the forms down to the base at several points across the slab, not just at the edge. Say the readings average 4.5 in because the base was graded low in the middle. Then:
- Depth = 4.5 in / 12 = 0.375 ft
- Volume = 100.00 sq ft x 0.375 ft = 37.50 cu ft
- Cu yd = 37.50 / 27 = 1.39 cu yd
Half an inch of extra depth over the whole slab is 0.15 cu yd more, 12.5 percent (1.389 against 1.235), which is more than the 8 percent overage covered on its own: 1.23 x 1.08 = 1.33, against 1.39 needed. The order of 1.5 cu yd still covers 1.39, but only because the round-up to a quarter yard added the rest. Averaging depth readings has its own pitfalls; see related: Averaging Readings: Mean, Median and Weighted.
Bagged instead. On a slab this size some crews mix from bags. The bag states its yield in cubic feet on the label, and that figure is what you divide by. An 80 lb bag of common premix yields about 0.6 cu ft; check the label of the product you are buying. At 0.6 cu ft per bag, 33.33 cu ft / 0.6 = 55.6 bags, so 56 before overage. That count tells you whether bagged is realistic: mixing and placing over fifty bags by hand is a long, heavy day for a small crew.
Hazard when mixing and placing: dry cement dust contains respirable crystalline silica and is alkaline, so mix bagged material outdoors or with ventilation, and where the dust calls for a respirator, use it under a written program per 29 CFR 1910.134 (applied to construction work by 29 CFR 1926.103). Wet concrete is caustic and burns skin over time: waterproof gloves, boots with pant legs outside them, and eye protection. Skin that has been in wet concrete gets washed with clean water promptly, and concrete in the eye gets flushed with clean water for at least 15 minutes, followed by medical attention.
Worked example 2: a mulch bed, 450 sq ft at 2 in
Line Item Value Unit
1 Area (decomposed beds) 450.00 sq ft
2 Depth 2 in
3 Depth / 12 0.167 ft
4 Volume = L1 x L3 75.00 cu ft
5 Cu yd = L4 / 27 2.78 cu yd
6 Check: L1 / 162 2.78 cu yd
Note line 4 used the exact depth (2/12 = 0.16667 ft), so 450 x 0.16667 = 75.00 cu ft. Using the rounded 0.167 gives 75.15 cu ft, which makes no difference here but shows why you carry the unrounded value forward and round only at the end. See related: Write the Calculation Down: The Field Math Habit.
The bed takes 2.78 cu yd. A yard that sells in half yards gets an order of 3.0 cu yd, and the 0.22 extra cu yd covers settling and a slightly heavy hand at the edges.
If the customer wants bags. Bagged mulch is commonly sold in 2 cu ft bags (check the bag). 75.00 cu ft / 2 cu ft per bag = 37.5, so 38 bags. Note that 27 / 2 = 13.5 bags make one cubic yard, which is a useful check: 2.78 cu yd x 13.5 = 37.5 bags.
What the depth means. Mulch settles. A bed spread at 2 in reads less after a few weeks of rain. If the customer expects 2 in that holds, some crews spread a little deeper. That is a depth decision for line 2, written down, not an extra yard tacked on at the end.
Gravel and stone: when the yard sells by the ton
Many yards sell aggregate by weight. Figure the cubic yards first exactly as above, then convert using the yard's own tons-per-cubic-yard figure for that product. Do not use a number from memory or from another supplier: density varies with the stone, the gradation and how wet the pile is, so the conversion belongs to the material in front of you.
Compacted base also needs more loose material than its finished volume, because compaction squeezes out voids. A 4 in compacted base needs more than 4 in of loose stone. Ask the yard what loose-to-compacted allowance they use for that product, or use the figure your own jobs have shown, and write it as its own line.
How to verify the order before you call it in
- The two methods agree. Line 7 (volume / 27) and line 8 (area / coverage) match to the second decimal. If they differ, check the depth conversion first; it is where most errors live.
- The answer is in the right neighborhood. A rough estimate from the coverage table: 100 sq ft at 4 in is a bit more than 81 sq ft, so a bit more than one yard. 450 sq ft at 2 in is close to three times 162, so close to three yards. If the mulch sheet says 8.3 or 0.23, something is off by a factor of 3 or 12.
- Every line has a unit. If line 6 says "33.33" with no unit, you cannot tell whether it is cubic feet or cubic yards, and the next person who reads the sheet will guess. See related: Units Carried Through Every Line of a Calculation.
- The overage and the round-up are separate lines. Anyone reading the order can see how much is material the job needs, how much is allowance, and how much is just the supplier's increment.
References
- The Measure and Takeoff Basics (library card)
- The Materials Waste Factor Worth Measuring (library card, for setting the overage)
- 29 CFR 1910.134, Respiratory Protection (OSHA; construction work has its own counterpart in Part 1926)
- See related: The Mulch Order That Came Three Times Too Big
- See related: Units Carried Through Every Line of a Calculation