Vertical walls: length × width × depth
For a trench with vertical walls, the cross-section is a rectangle, so the volume is the length times the base width times the depth:
Volume = L × W × D
A trench 20 m long, 0.6 m wide and 1.5 m deep holds 20 × 0.6 × 1.5 = 18.0 m³. Measure the depth from the ground surface to the base of the trench, and convert every dimension to metres before you multiply. Mixing millimetres and metres is an easy mistake to make.
Battered walls
When the sides are battered back, the cross-section is a trapezoid. Work out the width at the top first, then use the average of the top and bottom widths:
- Top width = base width + 2 × depth × H, for a batter of 1 vertical to H horizontal
- Volume = L × D × (base width + top width) ÷ 2
Take the same trench with both sides battered at 1V:1H. The top width is 0.6 + 2 × 1.5 × 1 = 3.6 m, the average width is (0.6 + 3.6) ÷ 2 = 2.1 m, and the volume is 20 × 1.5 × 2.1 = 63.0 m³. That's three and a half times the vertical-wall volume, which is why the wall shape matters as much as the trench size when you price the dig. If you're not sure how batter ratios are written, see slope ratios explained.
Benched walls
A benched excavation steps out in levels. Treat each level as its own rectangle and add them up. For a trench 3.0 m deep with a 1.2 m base, benched in three 1.0 m steps that each step out 1.0 m on both sides:
- Bottom level: 1.2 m wide × 1.0 m high = 1.2 m²
- Middle level: 3.2 m wide × 1.0 m high = 3.2 m²
- Top level: 5.2 m wide × 1.0 m high = 5.2 m²
The cross-section is 9.6 m², so every metre of trench is 9.6 m³ of excavation, and the trench is 5.2 m wide at the surface.
When the depth changes along the trench
Trenches rarely have the same depth for their whole length. Split the run into sections where the depth is roughly constant, or use the average end area method: work out the cross-section area at each end of a section, average the two, and multiply by the section length.
Volume = L × (A1 + A2) ÷ 2
From the hole to truck loads
The volumes above are the in-place, or bank, volume. Dug material bulks up, so it takes more room in a truck than it did in the ground. Multiply by a bulking factor for your material to get the loose volume. It varies a lot between sand, clay and rock, so take it from your geotechnical information or local experience rather than a rule of thumb.
For the 63.0 m³ battered trench, with an assumed bulking factor of 1.25, the loose volume is 63.0 × 1.25 = 78.75 m³. With trucks carrying 10 m³ each, that's 7.9 loads, so 8 truck loads. Check the truck's weight limit as well as its volume, because heavy material can reach the payload limit before the tray is full.
Backfill
Backfill is the trench volume minus whatever goes into the trench. For a pipe, subtract the volume it displaces:
Pipe volume = π × (outside diameter ÷ 2)² × length
A 20 m run of pipe with an outside diameter of 0.35 m displaces π × 0.175² × 20 = 1.92 m³, leaving 63.0 − 1.92 = 61.08 m³ to fill in the battered trench. Fill compacts, so you need more loose material than the space it fills. With a compaction factor of 1.2, order about 61.08 × 1.2 = 73.3 m³ of loose fill. Your supplier or specification gives the factor for your material, and zones such as the bedding and overlay may need different materials.
A note on wall shape
This article is about quantities. The wall shape you can use, whether vertical with shoring, battered or benched, depends on the ground, the depth and your work health and safety obligations. It should come from your engineer or geotechnical advice, not from the volume you'd like to dig.
Doing it on site
TrenchCalc works through all of this on your phone. Vertical, battered and benched walls, fill with its density and compaction factor, and truck loads are in the free version. Cement-stabilised zones, culverts and LiDAR scans are in the Lifetime unlock.