Cubic Yard Calculations
The geometry layer of earthwork estimating — the formulas that turn plan dimensions into bank cubic yards, from a slab to a mass-grading section. All computed methods (the average-end-area convention verified across DOT manuals), with the reminder that matters: pay lines are neat lines; production quantities add slope layback, working room, and over-excavation — estimate both numbers and know which one the contract pays.
The formulas
| Shape / method | Formula | Note |
|---|---|---|
| Slab / trench | CY = L(ft) × W(ft) × D(ft) ÷ 27 | 27 cu ft per cubic yard |
| Pit (four corners) | CY = plan area × average of corner depths ÷ 27 | Grid method for big areas: interior points ×4, edges ×2, corners ×1 |
| Average end area | V = (A₁ + A₂) ÷ 2 × L ÷ 27 | Cross-sections at 25–100 ft stations — the roadway/mass-grading standard |
| Sloped trench sides | Add the slope prisms: extra CY = D² × (H:V ratio) × L ÷ 27 per side | Neat-line volume is the floor of the estimate, never the answer |
From geometry to money
These formulas produce BCY; the conversions chart turns that into truck yards and fill yards, and the OSHA slopes that inflate the real dig live on the slope chart — the slope-prism row here is that chart wearing math. For site-wide balancing, the section method feeds the cut & fill reference.
Common questions
How do you calculate cubic yards of dirt?
Feet cubed, divided by 27. A trench 100 ft long, 3 ft wide, 5 ft deep is 100 × 3 × 5 ÷ 27 = 55.6 bank cubic yards — before slopes. The 27 is the whole trick (3 ft × 3 ft × 3 ft), and keeping every dimension in feet before dividing is the whole discipline.
What is the average end area method?
The roadway/mass-grading standard: take cut/fill cross-section areas at stations (25–100 ft apart), average each adjacent pair, multiply by the distance between them, divide by 27. V = (A₁+A₂)/2 × L ÷ 27. It slightly overstates volume between dissimilar sections — fine for pay quantities, and every DOT accepts it.
Why is the real dig bigger than the calculated volume?
Because the formula measures neat lines and the excavation has physics: OSHA slopes lay the walls back (a 5-ft-deep Type C trench adds a 7.5-ft layback each side), workers need room outside the pipe, and over-excavation for bedding is real yardage. A sloped trench often moves 2–4× its neat-line volume — price the dig, pay the neat line, and know which number is which.