Excavation Volume in Cubic Yards: Bank, Loose, and Compacted Calculations

The excavator finishes a basement dig at noon and the trucking sub asks, “How many loads?” If your excavation volume estimate priced the haul-off at 80 cubic yards bank but the soil swelled 30% on the way to the trucks, you’re actually paying for 104 loose yards. That’s three or four extra trips depending on truck size, and it’s your number to defend if the GC questions the bill.

Excavation volume calculations look like a simple length-times-width-times-depth problem. They’re not. The number you start with (bank volume) is not the number the trucks haul (loose volume), and neither equals the volume that ends up back in the trench when you backfill (compacted volume). This guide covers all three, with worked numbers for the soil types you actually encounter on a residential or light-commercial site.

Bank, Loose, and Compacted Volumes

Three different volumes describe the same dirt at different stages of its journey:

• Bank volume (BCY — bank cubic yards): the soil sitting undisturbed in the ground. This is what you measure from the plans — the difference between existing grade and proposed excavation grade. Bank volume is what the equipment digs out by depth and area.
• Loose volume (LCY — loose cubic yards): the soil after excavation, broken up and aerated. Always larger than bank. This is what you haul, and it’s what truck capacity is rated against.
• Compacted volume (CCY — compacted cubic yards): the soil after placement and compaction in a fill area. Smaller than bank for most soils. This is what matters when you’re calculating how much fill you need to bring in for a cut-and-fill grading job.

The calculator on a phone gives you bank volume. The trucking bill is in loose volume. The fill takeoff is in compacted volume. Mixing them up is how takeoffs go wrong.

Calculating Bank Volume from the Plans

For a flat-bottom excavation (basement, footing trench, slab subgrade), the basic formula is straightforward:

where L, W, and D are in feet, and the 27 converts cubic feet to cubic yards. For an excavation with sloped sides — which is most real digs over four feet deep, because OSHA requires it — you need to account for the additional volume in the slope.

For a sloped-side excavation, calculate the volume of the trapezoidal cross-section. For a rectangular dig with uniform side slopes:

where s is the slope ratio (horizontal run per unit of vertical rise — 1.5 for Type C soil at 1.5H:1V). The first term is the prism, the middle term is the four trapezoidal side wedges, and the last term is the four corner pyramids.

Average End Area Method (for Linear Excavations)

For roads, utility trenches, or any excavation where the cross-section changes along the length, use the average end area method. Take cross-sections at regular stations (typically every 25 or 50 feet), calculate the area at each station, then:

where A₁ and A₂ are the cross-section areas in square feet at the two stations and L is the distance between them in feet. Sum the segments to get total volume.

This method handles sloping terrain and irregular cuts that the prism formula can’t. For grading jobs with significant cut-and-fill balancing, it’s the only way to get a defensible quantity without a 3D model.

Apply the Swell Factor for Loose Volume

When soil is excavated, it breaks apart and the void space increases. The swell factor measures that expansion:

For a 100 BCY excavation in clay (35% swell): 100 × 1.35 = 135 LCY to haul off. That’s the number on the trucking quote.

If you don’t know the soil type before the dig — common on residential additions where there’s no geotech — budget loose volume at 30% swell as a default. Catch the actual soil at the first bucket and adjust if needed.

Worked Example: Basement Excavation Volume in Cubic Yards

The slope volume is the part takeoffs miss most often. On a 9-foot dig, the side allowance is roughly 9 LF on each side at the surface (for 1H:1V slope) — that’s a lot of dirt that doesn’t appear on the basement footprint. The percentage swing depends on footprint size: small residential basements (24’ × 40’ range) run 65–70% extra over straight-wall, mid-size like the example above lands near 55%, and larger commercial cuts (60’ × 100’ or bigger) drop to 30–40% because the slope wedges are smaller relative to the prism. Run the prismoidal formula for any dig that matters — a single percentage rule of thumb won’t hold across project sizes.

Compaction and Backfill

If the excavation includes a fill component — backfill against foundation walls, structural fill under a slab, or grade build-up — you need to plan for shrinkage when the loose dirt gets compacted in place. Typical shrinkage factors:

• Sand and gravel: 5–10% shrinkage from bank to compacted
• Silt and clay: 10–15% shrinkage from bank to compacted
• Engineered structural fill: 15–20% shrinkage (compacted denser than native bank)

The math: if you need 50 CCY of compacted fill in clay with 12% shrinkage, you need 50 / (1 − 0.12) = 57 BCY of native source material. If hauling that material in, the truck quantity is 57 × 1.30 (swell) = 74 LCY. The chain of unit conversions is what trips up most takeoffs.

Common Mistakes

1. Using bank volume for the trucking estimate. Trucks haul loose. Pricing 100 BCY of haul-off at 12 LCY per truck gives you 8 loads on paper, but you’ll actually need 11 trucks for the 130 LCY that came out of the ground.
2. Ignoring slope on excavations over 4 feet deep. OSHA-required slope adds significant volume on deeper digs. Skipping it is both a dollars problem and a safety-citation risk.
3. Assuming swell factor without identifying soil type. A 50% miss between sand (15% swell) and clay (35% swell) compounds across a large dig. If the geotech report or test pits aren’t available, talk to the excavator or someone who’s dug nearby before quoting.
4. Confusing swell and shrinkage. Swell goes from bank to loose; shrinkage goes from bank (or loose) to compacted. They’re different operations applied at different points in the workflow. The same 100 BCY of clay produces ~135 LCY of loose haul-off and only ~88 CCY when re-compacted as fill.
5. Mismatching truck capacity to soil density. A 12-yard tri-axle hauling wet clay will run at weight limit before it fills the box. For dense or wet soils, capacity is set by weight, not volume — check the local DOT’s legal axle loads before bidding the truck count.

What This Doesn’t Cover

Mass excavation on highway and infrastructure projects uses cut-and-fill optimization, mass diagrams, and grading software that computes earthwork from a 3D surface model. The hand methods above are appropriate for residential, light commercial, and small site work. For anything over a few thousand cubic yards, get a surveyor’s digital terrain model and run it through grading software.

Dewatering, rock excavation, and contaminated-soil disposal all carry their own quantity and pricing implications that aren’t in the bank/loose/compacted framework. Treat them as separate line items with their own unit costs.

Once the excavation is complete, the next quantities are foundation-side: concrete footing volumes for posts and piers, slab pours, and the drainage rock and backfill against the foundation walls. The retaining wall material estimate covers the case where a portion of the excavation is replaced by structural retaining walls rather than backfilled.