# Excavation Volume Calculator

Sloped pit volume: top, base and mid-section via the prismoidal formula.

- Page: https://jianzhujisuan.com/en/excavation-volume
- Category: Construction (https://jianzhujisuan.com/en/c/construction)
- Chinese version: https://jianzhujisuan.com/zh/excavation-volume.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Base length 40 m, Base width 30 m, Excavation depth 6 m, Slope ratio 0.75 m/m): **Excavation volume 9252 m³**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Base length | number | 40 | m |  |
| Base width | number | 30 | m |  |
| Excavation depth | number | 6 | m |  |
| Slope ratio | number | 0.75 | m/m | Horizontal run per 1 m of depth, e.g. 1:0.75 → 0.75 |

## Formula

- **Top size**: Ltop = Lbase + 2·m·H
- **Prismoidal volume**: V = H/6·(S1 + 4S0 + S2)
- **Mid-section**: S0 = (Lbase+m·H)(Bbase+m·H)

## Worked example

Base 40×30 m, 6 m deep, 1:0.75 slope: top 49×39 m, areas 1911 / 1200 / 1535 m², about 9252 m³.

### What one notch of batter costs (same pit: 30 × 20 m base, 5 m deep)

| Slope ratio m | Top size (m) | Excavation (m³) | Loose (m³, ×1.25) | 20 m³ truck loads | vs vertical cut |
|---|---|---|---|---|---|
| 0.00 | 30.0 × 20.0 | 3000 | 3750 | 188 | +0% |
| 0.33 | 33.3 × 23.3 | 3431 | 4288 | 215 | +14% |
| 0.50 | 35.0 × 25.0 | 3667 | 4583 | 230 | +22% |
| 0.75 | 37.5 × 27.5 | 4031 | 5039 | 252 | +34% |
| 1.00 | 40.0 × 30.0 | 4417 | 5521 | 277 | +47% |
| 1.25 | 42.5 × 32.5 | 4823 | 6029 | 302 | +61% |

Same base, same depth, only the batter changes from 0 to 1.25, and the volume goes from 3000 to 4823 m³ — **61% more soil, 114 more truck loads**. That is why the slope ratio is not a place to round up 'for safety': too steep is a safety problem, too flat is a cost problem, and both have to be counted. The loose column uses 1.25; real clay runs 1.2-1.3 and sand 1.1-1.15, so change it by soil type rather than applying 1.25 across the board. Note also that once the top size crosses the site boundary or reaches a neighbouring footing, the scheme changes from open cut to retention — soldier piles, anchors, props — which is a different sum entirely and outside this page's formula.


## Questions

### How do I choose the slope ratio?

By soil and depth. Hard plastic clay and silty clay can stand at 1:0.33-1:0.5; ordinary clay 1:0.5-1:0.75; loose sand and silt 1:1 or flatter. High groundwater and wet weather need flatter slopes or slope protection. If a deep pit cannot slope, use retention - forcing a steep slope causes collapse, one of the most fatal accident types.

### Why apply a bulking factor to the volume?

The prismoidal result is the in-situ (bank) volume. Excavated soil loosens and swells, so haulage is counted in loose volume, with a bulking factor of 1.2-1.3 (lower for clay, higher for sand). Apply it to the bank volume when booking trucks or signing spoil agreements, or the volumes will not reconcile and you eat the trucking cost.

### Should I add a working space before calculating?

Yes, and add it before applying the slope. What is being measured is the ground actually excavated, not the size of the foundation, so the base dimensions should first be offset by a working space: typically 300 mm per side where formwork is struck, 200 mm per side for brick footings, the outer face of any waterproofing, or the inner face of the retention system, plus room for a drainage trench and sump inside the pit. Fix base = footing + 2 × working space first, then apply the slope ratio to get the top size. Do it the other way round and the whole pit comes out undersized, dragging volume, truck loads and backfill with it - which usually ends in a second excavation and a second claim.
### Is it always safer to use a flatter slope?

Safer for the men, more expensive for the job. On the same 30 × 20 m base at 5 m deep, going from vertical to a 1.25 batter takes the volume from 3000 to 4823 m³ — 61% more soil and 114 extra 20 m³ loads. Too steep collapses, though, and the right batter depends on soil, depth, groundwater and surcharge at the crest. Spoil heaps, a parked excavator or heavy trucks along the edge add 20 kPa of surcharge, which is enough to bring down a slope that was otherwise fine.

### Can the volume be priced straight off?

Not straight off — it feeds three separate items: excavation in bank volume; disposal at bank volume × bulking factor, priced by the load; and backfill, which is the excavation minus the volume of footings and basement, then × a compaction factor. Three different measures. Priced as one rate on bank volume, the disposal and backfill both come up short. Then the working space: the base should be the footing outline plus 300 mm a side for formwork or 200 mm for brick footings, added before the batter is applied. Do it the other way round and the whole pit comes out small.


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