How to Calculate Excavation Volume with Slope

How do you calculate excavation volume?

For a rectangular vertical-sided excavation with a level bottom and level original surface, multiply the excavation length by width by vertical depth. Use the excavation dimensions, including any specified working space, rather than only the size of the footing, tank or structure. Keep all three dimensions in the same unit. The calculator converts metres, millimetres or feet to metres before calculating cubic metres. Separate excavations can be added only after checking they do not overlap.

Excavation volume calculator with slope

Choose the four-sided pit model when all four faces slope outward uniformly from a rectangular bottom. Enter the horizontal-to-vertical ratio for each pair of opposing faces: the width-direction ratio moves each long side outward, while the length-direction ratio moves each end outward. At height z above the bottom, the section is (L + 2 × mL × z) by (W + 2 × mW × z). Top length is L + 2 × mL × D and top width is W + 2 × mW × D. The bottom and top must be level, and the slopes straight and constant.

What does a slope of 1.5H to 1V mean?

For every metre of vertical depth, each affected face extends 1.5 metres horizontally outward. With 2 m depth, each side extends 3 m; two opposing sides therefore add 6 m to the top dimension. Enter 1.5, not 150, in the H:1V field. These are geometric ratios, not recommended excavation slopes. A ratio of zero represents a vertical face in the geometry only; it does not establish that a vertical face can stand safely.

Trench excavation with sloping sides

The trench model keeps both end faces vertical and applies the same entered outward slope to its two long sides. Its section area is D × (bottom width + mW × D); multiply by bottom length for volume. A pit with sloped ends needs the four-sided model instead. The trench model does not include ramps, benches, varying depths, curved alignments or additional end excavation. Calculate changes in geometry as distinct, non-overlapping sections or use survey quantities.

Prismoidal formula and the rectangular pit

The calculator uses V = D × (A bottom + 4 × A mid-depth + A top) ÷ 6 for the straight, uniformly sloped rectangular model. At mid-depth, dimensions are L + mL × D and W + mW × D. The section area varies quadratically with height, so this formula is exact for this ideal geometry. Multiplying the average of bottom and top areas by depth generally overestimates this four-sided model when both directions widen. The square-root frustum shortcut requires similar parallel sections and is not a universal formula for every sloped rectangular pit.

Worked soil excavation example

Suppose the bottom is 10 m long and 4 m wide, the vertical depth is 2 m, and each face uses an illustrative 1H:1V outward slope. The top is 14 m by 8 m, the mid-depth section is 12 m by 6 m, and the volume is 146.667 m³, rounded. The vertical-sided box with those bottom dimensions is 80 m³. This example shows the geometric difference only; it does not specify a safe slope for the site. A separately entered 20% swell gives 176 m³ loose volume.

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