Battered Pit Volume Calculator
Top dimensions and frustum volume from base size, depth and batter.
Inputs
Result
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.
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.
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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.