How do you calculate excavation volume with sloped walls?

Battered pits are wider at the top than the bottom, so a simple length times width times depth overstates the dig. This tool uses the average-area (prismoidal) method: it averages the top and bottom areas, multiplied by depth, which is exact for straight-sided sloped pits.

What is a swell factor?

Soil expands when excavated. A swell factor (or load factor) converts the in-place bank volume to loose volume. Common values are about 1.25 for sand, 1.30 for common earth, and 1.40 to 1.65 for clay or rock, so 100 bank cubic yards may haul as 130 loose cubic yards.

What is the difference between cut and fill?

Cut is material excavated and removed; fill is material placed back to bring an area up to grade. Net haul-away is cut minus fill. If fill exceeds cut, you must import material instead of hauling it away.

What side-slope ratio should I use?

It depends on soil stability and safety rules. A common safe batter is 1:1 (one horizontal to one vertical) for firm soil, or flatter such as 1.5:1 for loose or sandy ground. Always follow trench-safety regulations; shoring may be required instead of sloping.

Why convert to cubic yards?

Earthwork and trucking in the US are priced and dispatched in cubic yards. One cubic yard is 27 cubic feet. The tool reports both cubic feet, cubic yards, and cubic metres so you can match haul-truck capacities and quotes.

Excavation Cut & Fill Volume Calculator

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.

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.

Example and tips

A 20 × 12 ft footing pit dug 6 ft deep with a 1:1 batter has a bottom of about 8 × 0 ft — meaning a 1:1 slope is too steep for that depth and the bottom would pinch out, so the tool flags non-physical geometry. A gentler 0.5:1 batter gives a 14 × 6 ft bottom, averaging to about 1,524 cubic feet, or 56 bank cubic yards. With a 1.30 swell that hauls as roughly 73 loose cubic yards. Always keep twice the slope offset less than the smaller top dimension, or the walls meet before reaching depth.