How to Calculate Cubic Yards of Concrete (With Worked Example)

Calculating cubic yards of concrete is a five-step process — measure, convert, multiply, divide, add waste. Here's the entire chain on a real example, plus three more shorter examples for the other common shapes.

Worked example 1: 12 × 10 ft × 4 in patio slab

1. Convert the 4-inch thickness to feet: 4 ÷ 12 = 0.333 ft.
2. Multiply for cubic feet: 12 × 10 × 0.333 = 40 ft³.
3. Convert to cubic yards: 40 ÷ 27 = 1.48 yd³.
4. Add 10% waste: 1.48 × 1.10 = 1.63 yd³.
5. Round up to the nearest quarter yard: 1.75 yd³.

Sanity check: at about 4,050 lb per cubic yard, 1.75 yd³ weighs roughly 7,090 lb. That's about 80 of the 80-lb bags or a half-truck ready-mix delivery. Both numbers should feel right for a 120-square-foot patio.

Worked example 2: 12-in × 4-ft round footing

For a single 12-in diameter, 4-ft deep deck pier:

1. Convert diameter to feet: 12 ÷ 12 = 1 ft.
2. Compute radius squared: (1 ÷ 2)² = 0.25 ft².
3. Multiply by π and depth: π × 0.25 × 4 = 3.14 ft³.
4. Convert to cubic yards: 3.14 ÷ 27 = 0.116 yd³.
5. Add 10% waste: 0.116 × 1.10 = 0.128 yd³.

For a deck with twelve such piers, you'd need 12 × 0.128 ≈ 1.54 yd³. Bagged is cheaper here — that's roughly 70 of the 80-lb bags total.

Worked example 3: 18-in OD × 6-in ID × 36-in tall planter

For a hollow concrete planter with 18-in outer diameter, 6-in inner diameter, and 36-in height:

1. Convert all to feet: OD = 1.5 ft, ID = 0.5 ft, h = 3 ft.
2. Outer cylinder volume: π × (1.5/2)² × 3 = π × 0.5625 × 3 = 5.30 ft³.
3. Inner void volume: π × (0.5/2)² × 3 = π × 0.0625 × 3 = 0.589 ft³.
4. Net concrete: 5.30 − 0.589 = 4.71 ft³.
5. Cubic yards: 4.71 ÷ 27 = 0.175 yd³ → 0.20 yd³ with waste.

Worked example 4: 4-step concrete stoop

For a 4-step concrete stoop with 7-in rise, 11-in run, 36-in width, and a 12-in deep top platform:

1. Convert everything to feet: rise = 0.583, run = 0.917, width = 3.0, platform_depth = 1.0.
2. Compute the wedges: each step i contributes i × rise × run × width = i × 0.583 × 0.917 × 3 = 1.604i ft³.
3. Sum for 4 steps: 1.604 × (1 + 2 + 3 + 4) = 1.604 × 10 = 16.04 ft³.
4. Add platform: 1.0 × (4 × 0.583) × 3.0 = 7.0 ft³.
5. Total: 16.04 + 7.0 = 23.04 ft³ → 0.85 yd³ → 0.95 yd³ with waste.

Quick-pick reference

Common pre-calculated cubic-yard totals (without waste margin) so you can sanity-check your own numbers:

• 10 × 10 ft × 4 in patio: 1.23 yd³
• 12 × 12 ft × 4 in patio: 1.78 yd³
• 16 × 24 ft × 4 in garage floor: 4.74 yd³
• 20 × 20 ft × 4 in driveway: 4.94 yd³
• 20 × 20 ft × 6 in heavy driveway: 7.41 yd³
• 4 × 50 ft × 4 in sidewalk: 2.47 yd³
• 50 ft × 16 in × 12 in footing trench: 2.47 yd³

For a live calculation with all conversions handled, see the yard calculator or the full concrete calculator. For the same math worked through different shapes side-by-side, see how to calculate concrete.