Trench/Ditch Volume Calculator

Working out ditch excavation volume is the first job on any drainage channel, irrigation ditch, utility trench or foundation perimeter. A ditch is rarely a plain rectangle in section. The banks are cut back at an angle, called the batter or side slope, so the walls hold themselves up, and that turns the cross-section into a trapezoid.

Trapezoidal cross-section volume formula:

Cross-Section Area = (Top Width + Bottom Width) ÷ 2 × Depth

Volume = Cross-Section Area × Length

Side slope (batter) calculation: A slope expressed as H:V (horizontal : vertical) means the bank steps out H units for every 1 unit of depth.

Top Width = Bottom Width + (2 × Depth × Slope Ratio)

Soil type sets both the slope and the weight:

Wet soil being the heaviest on that list surprises people. The water is not displacing anything, it is filling voids that were full of air, so saturated ground can weigh a fifth more than the same soil in August. It is also the least stable, which is why it wants the flattest banks.

Swell, and why the pile is bigger than the hole

Soil in the ground is compacted by everything that has ever sat on top of it. Dig it out and it breaks up, air gets in, and the same material takes up more room. That expansion is the swell factor, and it is the number that decides how many truck loads you need, not the trench volume.

Typical figures: sand and gravel swell 10 to 15%, common loam 20 to 25%, and stiff clay 30 to 40%. Blasted rock is the extreme case at 50 to 60%. If you are hauling the spoil away, work off the swelled volume. If you are backfilling with it, remember you will have material left over even after it settles back, because it never returns to bank density.

The weight does not change, only the volume. A ton in the trench is still a ton in the truck.

Worked example: An irrigation ditch, 200 metres long, 0.8 m deep, 0.5 m bottom width, in sandy clay on a 1:1 slope:

• Top width: 0.5 + (2 × 0.8 × 1) = 0.5 + 1.6 = 2.1 m
• Cross-section area: (2.1 + 0.5) ÷ 2 × 0.8 = 1.04 m²
• Volume: 1.04 × 200 = 208 m³ in the ground
• At 1,750 kg/m³ for sandy clay: 364 tonnes of spoil
• With 25% swell, that 208 m³ becomes 260 m³ of loose material to cart away

Cost estimation (rough US figures for 2025, and they vary enormously by region):

• Small excavator: $100 to $200 an hour, moving 40 to 80 m³ an hour
• 208 m³ ÷ 60 m³/hr = about 3.5 machine hours, so $350 to $700 to dig
• Offsite spoil disposal, if you cannot use it on site: add $10 to $25 a tonne, which on 364 tonnes swamps the excavation cost entirely

That last point is worth sitting with. On most jobs the digging is cheap and the getting-rid-of-it is not. Finding somewhere on site to spread or berm the spoil is usually the single biggest saving available.

Trench safety. Anything deeper than 5 feet (1.5 m) that people will enter needs a protective system, either sloped banks or a shoring box, under OSHA and its equivalents elsewhere. A cubic metre of soil weighs about as much as a small car, and trench walls fail without warning. The slope ratios in the table above are minimums for stable, undisturbed ground, and previously excavated ground is not stable ground.

Dewatering note: If the ditch bottom will sit below the water table, budget for pumping during and after the dig, and expect the walls to want a flatter batter than the table says.