# Battered Pit Volume Calculator

Top dimensions and frustum volume from base size, depth and batter.

- Page: https://jianzhujisuan.com/en/pit-volume
- Category: Area and volume (https://jianzhujisuan.com/en/c/area-volume)
- Chinese version: https://jianzhujisuan.com/zh/pit-volume.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Base length 10 m, Base width 8 m, Depth 3 m, Batter ratio m 0.5): **Excavation volume 329.96 m³**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Base length | number | 10 | m |  |
| Base width | number | 8 | m |  |
| Depth | number | 3 | m |  |
| Batter ratio m | number | 0.5 | — | Slope 1:m — sand 0.5-1.0, stiff clay 0.33 |

## 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

## Worked example

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.

## Questions

### 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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