Rectangular cut or fill
The simplest earthwork: a flat-bottomed excavation or a flat-topped fill of uniform depth. Volume = length × width × depth. In cubic feet, divide by 27 for cubic yards. A 100 × 50 ft excavation at 2 ft depth:100 × 50 × 2 = 10,000 ft³ ÷ 27 ≈ 370 CY
Use this for bulk grading, parking-lot subgrade, pad areas without sloped sides. For irregular cuts with varying depth, switch to the grid method (see the cut and fill guide).
Trench with sloped walls
Utility trenches deeper than 5 feet in unstable soil require sloped walls (OSHA 1926 Subpart P). The trench cross-section is a trapezoid: bottom width b, top width b + 2sh (where s is the H:V slope ratio and h is the sloped portion height), and the volume per linear foot is the trapezoid area times the length.
For a trench with full-depth slopes (no vertical lower portion):Cross-section area = b × d + s × d²For a benched profile with a vertical lower wall of height v:Cross-section area = b × d + s × (d − v)²
OSHA slope categories (rough rules of thumb — geotech governs):
- Stable rock — vertical walls (no slope) OK
- Type A — 0.75:1 max (cohesive clay)
- Type B — 1:1 max (granular cohesive, harder shale)
- Type C — 1.5:1 max (sandy, granular, unstable)
At 1:1 slope, a 6-ft-deep trench with a 2-ft bottom width opens to 2 + 2 × 1 × 6 = 14 ft at the surface — seven times the bottom width. The excavation volume is much larger than vertical-wall math suggests. Always bid sloped trenches against the actual excavation volume, not the bottom-width volume.
Building pad
A building pad is a layer of structural fill placed on prepared subgrade, usually compacted to a specified density. Volume = length × width × thickness. A 40 × 30 ft pad at 12 inches:40 × 30 × 1 = 1,200 ft³ ÷ 27 ≈ 44 CY
Pad volume is straightforward — the gotcha is that pad fill is typically imported select-fill material at a higher unit price than on-site cut. Bid pad fill against the import unit price, not the cut unit price.
Stockpile
Stockpile volume depends on the pile shape. Two approximations cover most cases:
Cone (round pile)
Volume = π × r² × h / 3 where r is the base radius and h is the pile height. A 15-ft radius, 10-ft tall pile:π × 15² × 10 / 3 ≈ 2,356 ft³ ÷ 27 ≈ 87 CY
Rectangular wedge (long pile)
Volume = length × width × average height. The average height usually approximates the centerline ridge height (a triangular cross-section gives an average that's half the ridge height; a more rectangular pile is closer to the ridge height itself).
Both approximations are rough. Real stockpiles have irregular shapes from how trucks dumped and pushed the material. For real stockpile measurement from drone imagery, use surface-based software that triangulates the point cloud and integrates volume from the surface down to a reference plane.
Density and tonnage
Mass = volume × density. The default 1,660 kg/m³ (~2,800 lb/CY) covers compacted earth at moisture equilibrium. For trucking capacity calculations, you usually want loose density (1,400- 1,600 kg/m³ for ordinary site soil). For pile foundation design or weight-critical hauling, use a tested geotech density.
Conversion: 1 short ton = 907.185 kg ≈ 2,000 lb. 1 tonne (metric ton) = 1,000 kg ≈ 2,205 lb. US suppliers price by short ton; international by tonne. Be explicit about which.
Translating volume into bid line items
A typical earthwork bid has separate unit prices for:
- Excavation — priced per bank CY (or loose CY on some bids). The volume of soil dug out of the ground.
- Off-site haul — priced per loose CY or per ton. The volume or mass moved off-site.
- Structural fill placement — priced per compacted CY. The volume of fill placed and rolled in.
- Import select fill — priced per bank CY (delivered). For pads and structural fill.
- Topsoil strip and re-spread — priced per CY or per square foot. The topsoil pulled before structural cut and put back after.
The volume calculator gives you bank volumes for cut, fill, and pad. Apply swell to get hauled loose CY. Apply shrink to get compacted CY for structural fill placement. Apply density to get tonnage if the unit price is per ton.
Verification on the job
Track haul truck counts during construction and reconcile against your bid. A tandem-axle dump holds 10-14 CY loose; a tri-axle holds 14-18 CY. Counted loads × truck capacity should match your bid volume within 5-10%. Beyond that, either your bank-to-loose factor was off or there was an unbudgeted scope item (over- excavation, unsuitable material removal). Use the variance to recalibrate your next bid.