Earthwork volume on a sloped pit is more than length times width times depth, because the walls splay outward toward the top. This calculator uses the average-area prismoidal method for battered excavations, then applies a swell factor and your backfill to give the bank cut, the fill-back, and the loose volume that actually leaves the site.
Why slope matters more than you might expect
A vertical-wall calculation on a battered pit systematically overstates the true dig volume. For a small footing pit the error may be minor, but for large site grading projects — where slope ratios of 1:1 or 1.5:1 across hundreds of feet produce much larger top-to-bottom area differences — using the wrong formula can over-order trucks, over-pay for soil disposal, and misestimate the time needed to complete the cut.
The average-area (prismoidal) method is the standard used by civil engineers precisely because it handles straight-sided truncated shapes exactly. It is not an approximation — for a frustum shape (the geometric solid produced by a battered pit) the average of top and bottom areas times depth gives the exact volume.
How it works
For a pit with a top opening that batters outward at a side slope s (horizontal run per unit of depth), the bottom is smaller than the top by twice the slope offset on each side. The volume is the average of top and bottom area times depth:
bottom length = top length − 2 × slope × depth
bottom width = top width − 2 × slope × depth
top area = top length × top width
bottom area = bottom length × bottom width
bank cut (cf) = (top area + bottom area) / 2 × depth
loose cut = bank cut × swell factor
net haul-away = loose cut − fill-back (loose)Cubic yards are cubic feet divided by 27; cubic metres are cubic feet times 0.0283168.
Worked example
Footing pit: 20 × 12 ft at the top, 5 ft deep, with a 0.5:1 batter.
bottom length = 20 − (2 × 0.5 × 5) = 15 ft
bottom width = 12 − (2 × 0.5 × 5) = 7 ft
top area = 240 sq ft
bottom area = 105 sq ft
bank cut = (240 + 105) / 2 × 5 = 862.5 cubic feet ≈ 32 bank CY
loose cut = 32 × 1.30 (common earth swell) ≈ 41.6 loose CYIf 10 bank CY of that material will be backfilled around the foundation, the net haul-away is roughly 32 – 10 = 22 bank CY, or about 29 loose CY to load onto trucks.
Swell factor reference
| Soil type | Typical swell factor |
|---|---|
| Sandy soil | 1.10 to 1.20 |
| Common earth | 1.25 to 1.35 |
| Clay | 1.30 to 1.45 |
| Broken rock | 1.50 to 1.65 |
The swell factor converts bank measure (in the ground) to loose measure (on a truck). It matters for ordering the right number of haul trucks and tipping loads. Note that compacted fill back in the pit uses a shrinkage factor (typically less than 1.0), but this tool applies swell to the cut volume and treats backfill as a bank volume subtracted before the swell conversion.
Always check twice the slope offset against the smaller pit dimension before committing to a batter — if the walls converge before reaching design depth, the geometry is non-physical and the tool will flag it.