Battered Pit Volume Calculator
Top dimensions and frustum volume from base size, depth and batter.
Quick answer
With the default inputs: Base length 10 · Base width 8 · Depth 3 etc.Excavation volume 329.96 m³
Edit the inputs below to recalculate.Inputs
Result
Excavation volume
329.96m³
| Top length | 13.00m |
| Top width | 11.00m |
| Batter width each side | 1.50m |
| Base area | 80.00m² |
| Top area | 143.00m² |
| Vertical-sided volume | 240.00m³ |
| Extra volume from batter | 89.96m³ |
| Increase over vertical | 37.5% |
| Loose volume at Ks 1.2 | 395.95m³ |
| Loads in a 12 m³ truck | 33loads |
Volume uses the frustum formula V = h/3 × (A1 + A2 + √(A1A2)), the standard for a rectangular frustum — averaging the two areas differs by 1-3%. The batter ratio m means m metres horizontally per metre of depth, i.e. a slope of 1:m. Pits deeper than 5 m need a designed support system, not just a batter.
Reverse: known result, work out one input
Enter a target result; the other inputs stay fixed and this one is worked out.
Formula
| Batter width | b = m × h |
| Top dimensions | L + 2b and W + 2b |
| Frustum volume | V = h/3 × (A₁ + A₂ + √(A₁A₂)) |
| Vertical volume | V = A₁ × h |
| Batter allowance | V = frustum − vertical |
| Loose volume | V = excavated × Ks |
A 10 × 8 m pit, 3 m deep, battering at 0.5: 1.50 m per side, a 13 × 11 m top, 329.96 m³ excavated — 37.5% more than the 240.00 m³ vertical case, or 33 truck loads.
How to work it out
- Set the battering coefficient m first: the horizontal spread per side divided by depth. It is about 1.0 for sand, 0.5-0.75 for stiff clay and 0.33 for hard soil. Take it from the ground investigation, not from habit.
- Spread per side b = m × h. At 3 m depth with m = 0.5 each side widens 1.5 m, turning a 10×8 m base into 13×11 m at the top.
- Compute both areas: base and top.
- Use the frustum formula V = h/3 × (A_base + A_top + √(A_base × A_top)). It is exact for a rectangular frustum; multiplying an average area by depth is not.
- The extra from battering is V − base area × depth, typically 30-60% additional excavation — useful for judging the cost impact.
- Bulked volume for disposal = V × Ks, with Ks normally 1.2-1.3. Excavated soil occupies 20-30% more than in situ, and haulage and disposal are priced on the bulked volume.
Where it goes wrong
- Using base area × depth. At 3 m with m = 0.5 the batter adds over 50%, so a vertical-wall assumption halves both excavation and haulage.
- Using average area × depth. The true frustum volume is slightly smaller, and on deep pits the error reaches 3-5% — hundreds of thousands on a large job.
- Taking m = 0.5 across the board. Sand needs 1.0 and 0.5 will collapse; hard clay at 1.0 wastes enormous volume. It must follow the soil type, and depths beyond 5 m require a designed support system.
- Pricing disposal on in situ volume. Excavated soil bulks 20-30%, so truck loads and disposal fees computed on in situ volume fall well short.
Material and cost
Excavation runs 25-60 CNY/m³ including plant and hand trimming but excluding haulage; haulage 20-50 CNY/m³ by distance; disposal 10-30 CNY/m³. Support is separate: soil nails 150-300 CNY/m², piles and anchors 400-800 CNY/m². Pits deeper than 5 m need a designed support scheme that can exceed 50% of the earthworks cost.
On site
- Battering is not always possible. Tight sites, adjacent buildings or buried services force a supported vertical face, so the volume is vertical but the support cost is added.
- Where groundwater is high, dewater before excavating. Working wet halves productivity and invites collapse, and dewatering is a separate cost item.
- Earthwork balance matters: if suitable excavated material can be reused as backfill, both haulage out and import are avoided. Work this out at planning stage.
- Leave 200-300 mm at formation level for hand trimming. Machine excavation to level disturbs the in-situ soil and reduces bearing capacity.
Basis
- GB 50854-2013 Standard method of measurement for building and decorative works, earthworks
- GB 50202-2018 Standard for acceptance of construction quality of building foundations
- JGJ 120-2012 Technical specification for retaining and protection of building foundation excavations
FAQ
Why does battering add thirty percent to the volume?
Because the batter forms a wedge ring around the pit whose area grows with the square of depth. At 3 m with a 0.5 batter each side opens 1.5 m, taking the top from 80 m² to 143 m² — 37.5% more volume. That is why a supported vertical excavation can cost less overall: the support is paid for, but excavation and cart-away drop, so compare totals.
How is the batter ratio chosen?
From the soil and the depth: dense sand about 0.5, silt and clay 0.33-0.5, soft soil or deep pits 0.75-1.0. The deeper the cut, the flatter the batter must be, because the slip surface moves down with depth. Codes also require a designed support beyond 5 m depth, or with surcharges or groundwater at the edge.
Does the working space at the base count?
Yes. Construction needs room around the structure — typically 300-600 mm per side, and 800 mm or more where there is formwork or waterproofing. Add the working space to the base dimensions before computing the batter; forgetting it produces a pit the crew cannot work in, and the rework costs far more than the extra excavation.
Cite this page
Use this format in reports, method statements or coursework. The link is permanent.
Building Calculator. Battered Pit Volume Calculator. 2026-10-25. https://jianzhujisuan.com/en/pit-volume
Results are estimating aids only and are not a design basis. Construction and final accounts must follow the drawings, the applicable standards and an approved method statement. Anything affecting structural safety, shoring or falsework must be checked by a suitably qualified engineer.