Excavation volume:
trench length × width × depth, and what changes it

The trench as a long box

A straight trench with vertical sides and a flat bottom is a rectangular box lying on its side. Its volume is the length, times the width, times the depth. The same arithmetic covers foundation trenches, drain runs, cable ducts and pipe trenches, as long as the sides can be treated as vertical.

That figure is called the bank, or in-place, volume. It is the size of the hole.

Why the spoil is bigger than the hole

Soil in the ground is packed together. Once it is dug, it fills with air, and the same material takes up more room in a heap or a lorry. The increase is called bulking or swell, and it varies a lot between sand, clay, rock and topsoil, so use a figure from your contractor or a geotechnical report.

The 25% used here is only an illustration. Sandy soils swell less, heavy clay swells more, and compacting the fill back will reduce the volume again, though never entirely to the original.

Working space and sloping sides

The theoretical width is the width of the footing or pipe. Digging that width precisely is rarely practical, because people need room to place formwork, lay pipe and compact. A working allowance on each side adds to the width, and a deep trench in loose soil may need sloped sides or support.

The sloped trench is a trapezoid in cross-section, so its area is the average of the top and bottom widths times the depth. The difference between the first and second rows is 21.6 m³, which is worth many extra lorry loads.

Trenches for pipes and cables

Services trenches follow the same rule, but their dimensions are driven by the pipe and the cover requirement rather than a footing. The depth is the cover above the pipe, plus the pipe diameter, plus any bedding below it. The width is the pipe diameter plus clearance either side so that the pipe can be laid and the sides compacted.

The cover requirement depends on the service and the location, so a drain under a driveway may need more than one in a garden. Use the figure in the relevant standard or the utility's own specification, and remember that bedding and surround material is a second quantity to order on top of the excavation.

The reverse sum: concrete and backfill

Part of the hole is refilled. A strip footing 0.3 m deep in the same 0.7 m by 30 m trench takes 30 × 0.7 × 0.3 = 6.3 m³ of concrete. Subtract that from the hole, and the remainder is the space for masonry below ground and backfill, with spare soil removed from site.

A concrete volume tool applies the same length, width and depth multiplication, so it works as a quick check on the footing and on the excavation itself. Use it for each stage and keep a note of the assumption on which each figure rests.

1. 1Excavation volume in place.
2. 2Concrete or pipe bedding volume in the hole.
3. 3Backfill volume = hole − structure.
4. 4Spoil to remove = in-place excavation − reusable backfill, adjusted for bulking.

A short method for site estimates

On site you often need a figure within minutes, with a tape, a notepad and a rough plan. The routine below keeps the estimate honest without a spreadsheet.

1. 1Pace or tape the centreline and write the length in metres.
2. 2Measure the width at the bottom of the trench and add the working space on each side.
3. 3Take depth at both ends and the middle, then use the average.
4. 4Multiply the three and write the result as in-place volume.
5. 5Multiply by 1.2 to 1.3 for the bulked volume unless you have a better swell figure for that soil.

Double-check the answer with a different route if the stakes are high, such as dividing the trench into 5 m sections, calculating each one, and adding them. If the two totals disagree by more than a few per cent, there is an arithmetic slip or a measurement that needs repeating.

Mistakes that distort the sum

The most common problem is using the wrong width: the structure width instead of the dug width. The next is a mixed unit, for example centimetres in one factor and metres in the others, which gives an answer a hundred times out. A third is forgetting that the starting ground level is rarely flat, so the depth varies along the run.

• Take depth readings at several points and average them for long trenches on sloping ground.
• Include extra length for pits at pipe junctions, valve chambers and inspection points.
• Keep topsoil and subsoil separate if the site rules require it; they are different quantities.
• Record the assumed swell factor so that a later estimate does not use a different one.