About this calculator
This calculator estimates the earthworks for a rectangular pit (a basement or a pad foundation) or a straight trench (a strip foundation, a drain or a service run). It gives the volume of soil dug out in its natural, in-place state (bank volume), the larger loose volume once the soil swells, the compacted backfill left once the foundation is in, and how much soil has to be hauled away and how much fill imported, with truck loads for each.
You choose where the backfill comes from: either all spoil is hauled away and the fill is imported (the default), or the excavated soil is reused for the backfill on site and only the rest is hauled away.
The dimensions you enter are those at the bottom of the excavation: length L, width W and depth D. The sides can be vertical (the default) or sloped. For a slope you give the horizontal distance per 1000 mm of depth: 0 means vertical sides, 500 means 0.5:1, and 1000 means 1:1.
Formula
Let k = side slope / 1000 (horizontal per vertical). Each sloped side sets back by k × D at ground level, so the width at ground level is:
top width T = W + 2 × k × D
Pit. All four sides are sloped, so the shape is a prismoid: two parallel rectangles joined by flat sloping faces. The prismoidal formula gives its volume exactly:
A_bottom = L × W
A_mid = (L + k×D) × (W + k×D)
A_top = (L + 2k×D) × (W + 2k×D)
V = D / 6 × (A_bottom + 4 × A_mid + A_top)
= D × (L×W + k×D×(L + W) + 4/3 × k² × D²)
Trench. Only the two long sides are sloped. Both ends are taken as vertical, so the trench is a trapezoid cross-section run along the length L:
V = L × D × (W + k×D)
Swell, backfill and shrinkage. The swell factor turns bank (in-place) volume into loose volume. The shrinkage factor turns bank volume into compacted volume: at 90 %, 1 m³ of soil in place gives 0.90 m³ once compacted.
swell = 1 + swell% / 100 (bank → loose)
shrinkage factor = shrinkage% / 100 (bank → compacted)
loose volume = V × swell (all excavated soil)
backfill = V − foundation volume (compacted)
bank needed = backfill / shrinkage factor
Reuse the excavated soil for backfill.
bank reused = bank needed
haul away, loose = (V − bank reused) × swell
haul truck loads = round UP (haul away / truck capacity)
If the bank volume needed is larger than V, there is not enough excavated soil and the calculator shows an error.
Haul all spoil away and import fill (the default).
haul away, loose = V × swell
imported fill = bank needed × swell (loose)
haul truck loads = round UP (haul away / truck capacity)
import truck loads = round UP (imported fill / truck capacity)
Truck loads are always rounded up: a part load is still a trip.
Worked example
A pit with a bottom of 10 m × 8 m, 2 m deep, 1:1 side slopes (side slope 1000), 25 % swell, a 90 % shrinkage factor, 10 m³ trucks and a 50 m³ foundation:
top = (10 + 2×2) × (8 + 2×2) = 14 m × 12 m
A_bottom = 80 m², A_mid = 12 × 10 = 120 m², A_top = 168 m²
V = 2 / 6 × (80 + 4×120 + 168) = 728 / 3 ≈ 242.67 m³
loose = 242.67 × 1.25 ≈ 303.33 m³
backfill = 242.67 − 50 = 192.67 m³ (compacted)
bank needed = 192.67 / 0.90 ≈ 214.07 m³
All spoil hauled away, fill imported:
haul away = 303.33 m³ → round up (303.33 / 10) = 31 loads
imported fill = 214.07 × 1.25 ≈ 267.59 m³ → round up (267.59 / 10) = 27 loads
Excavated soil reused for backfill:
not reused = 242.67 − 214.07 ≈ 28.59 m³ (bank)
haul away = 28.59 × 1.25 ≈ 35.74 m³ → round up (35.74 / 10) = 4 loads
FAQ
What side slope should I enter? That depends on the soil, the depth, how long the excavation stays open and the safety rules where you build. The calculator does not suggest a value. It defaults to vertical sides (0), and you enter the slope your site requires.
Why is the loose volume larger than the excavation volume? Soil that is dug out loosens and takes up more space than it did in the ground. The swell percentage is an estimate that depends on the soil type and its moisture. The default of 25 % is only a starting point, so change it if you have better data for your soil.
Is the backfill figure the amount of soil to order or keep? No. Backfill is the compacted volume of the space around the foundation. To fill it you need more soil in place than that: the bank volume needed is backfill ÷ shrinkage factor. If you import the fill, the loose volume to order is that bank volume × swell. The shrinkage factor of 90 % is only an estimate, so change it if you have better data for your soil and compaction.
Which backfill source should I choose? Choose "Reuse excavated soil" if the excavated soil is suitable and stays on site for the backfill; only the rest is hauled away. Choose "Haul all spoil away, import fill" if all spoil leaves the site and the backfill is delivered, for example sand or gravel. Importing is the default because it gives the same haulage figures as earlier versions of this calculator, where all spoil was counted as hauled away. With no foundation and a shrinkage factor below 100 %, reusing the soil needs more soil than was dug, so the calculator shows an error.
Why are the trench ends vertical? Most trenches are long and narrow, so the ends make up a very small share of the volume. Treating them as vertical keeps the input simple. For a short, wide excavation with all sides sloped, use pit mode instead.
Assumptions and limits
- The excavation is rectangular in plan with a flat, level bottom and level ground at the top. Every sloped side uses the same slope.
- In trench mode only the long sides are sloped, and both ends are vertical.
- The swell percentage, shrinkage factor, truck capacity and side slope are your own inputs, not values taken from a standard. The default swell of 25 % and the default shrinkage factor of 90 % are estimates: the real values depend on the soil, its moisture and the compaction achieved. No table of soils is used.
- Backfill is the compacted volume of the space around the foundation. Imported fill is assumed to have the same swell and shrinkage factors as those entered.
- The same truck capacity is used for hauling away and for importing.
- No standard is cited: the volumes come from plain geometry (a prismoid and a trapezoidal prism), and no code clause governs them.
- Safe side slopes and the shoring of excavations are a site-safety matter governed by local regulations and ground conditions. This calculator does not check them.