Excavation volume = length × width × depth for vertical sides. A trench 10 m long, 1 m wide and 1.5 m deep is 15 m³ in the ground; common earth swells about 25% when dug, so you haul 18.75 m³: 2 loads in a 10 m³ truck. Sloped sides use the prismoidal formula.
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Excavation (bank volume)
15.00m³
Loose volume to haul
18.75 m³
Truck loads
2 loads
Top of excavation
10.00 × 1.00 m
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Bank volume = L × W × D = 10.00 × 1.00 × 1.50 = 15.00 m³
Loose volume = 15.00 × (1 + 25%) = 18.75 m³
Truck loads = ⌈18.75 ÷ 10.0⌉ = 2
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Formulas
Vertical sides: V = L × W × DSloped sides: V = D/6 × (A_bottom + 4 × A_mid + A_top) top length = L + 2 × slope × D (same for width)Loose volume = V × (1 + swell %)Truck loads = ⌈ Loose volume ÷ truck capacity ⌉
Slope is horizontal distance per 1 vertical (1:1 = 45°).
Worked Examples
Trench with vertical sides: 10 m × 1 m × 1.5 m deep, common earth, 10 m³ trucks.
Bank volume = 10 × 1 × 1.5 = 15.00 m³
Loose volume = 15.00 × 1.25 = 18.75 m³
Truck loads = ⌈18.75 ÷ 10⌉ = 2 loads
Pit with 1:1 sloped sides: 2 × 2 m at the bottom, 1 m deep.
Top = 4 × 4 m (16 m²), mid-depth = 3 × 3 m (9 m²), bottom = 4 m²
V = 1/6 × (4 + 4 × 9 + 16) = 9.33 m³, more than double the 4 m³ of a vertical-sided pit
Typical Swell of Excavated Soils
Material
Swell (bank → loose)
10 m³ in the ground becomes
Sand / gravel
10–15%
11.0–11.5 m³
Common earth
20–30%
12–13 m³
Clay
30–40%
13–14 m³
Blasted rock
50–65%
15–16.5 m³
These are typical planning values; your geotechnical report or earthworks contractor will have site-specific figures.
Assumptions
Rectangular excavation with the same slope on all four sides.
Volumes are bank (in-situ) unless labelled loose. Compacted backfill shrinks below bank volume.
Safety: excavations deeper than about 1.2–1.5 m need shoring, battering or a trench box under most regulations.
Frequently Asked Questions
How do I calculate excavation volume?
For vertical sides, multiply length × width × depth. For sloped sides, use the prismoidal formula V = D/6 × (A_bottom + 4 × A_mid + A_top), where each A is the plan area at that level.
What is swell factor in excavation?
Soil takes up more space after it is dug because it loosens. Bank (in-place) volume × (1 + swell %) gives the loose volume you load into trucks. Typical swell is 10–15% for sand, about 25% for common earth, 30–40% for clay and 50% or more for blasted rock.
How many truck loads will I need?
Divide the loose volume by the truck's heaped capacity and round up. A 15 m³ excavation in common earth is 18.75 m³ loose, or 2 loads in a 10 m³ truck.
What side slope should I use?
It depends on the soil, depth, water and your local safety rules. As a guide, stiff clay may stand at ¼:1 to ½:1, average soils at 1:1 and loose sand or gravel at 1½:1. Deep excavations need a temporary works design.
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