Excavation Calculator
Cubic yards of material to be dug out — including battered side walls, over-excavation and swell. How it works
Excavated volume
cubic yards
Bank measure
- Cubic feet
- 19,200cu ft
- Cubic metres
- 543.7m³
- Area at grade
- 2,400ft²
You have modelled vertical walls at 5 ft or deeper. Excavations that people enter at that depth normally require sloping, benching or shoring — check the requirements that apply to your site and add a side slope ratio if the walls will be laid back.
This is bank volume — the material as it sits in the ground. It will occupy more space once it is dug. Add your swell factor to see the loose volume you actually have to haul.
Show the calculationHide the calculation3 steps
The working
Base area = L × W
= 60 ft × 40 ft
= 2,400 ft²
Volume = Base area × Depth
= 2,400 ft² × 8 ft
= 19,200 cu ft
Cubic yards = Cubic feet ÷ 27
= 19,200 ÷ 27
= 711.1 cu yd
Enter the dimensions of the hole at the bottom of the cut. If the walls are benched or battered rather than vertical, add the side slope ratio and the calculator uses the prismoidal formula instead of a flat box, which is where most quick estimates go wrong.
How this calculator works
Only your inputs and exact unit conversions. Where a figure comes from anywhere else, it is recorded below with its source.
- Formula version
- 1.0.0
- Last reviewed
- 2026-08-14
- External data
- None
- Category
- Earthwork
What this calculates
The in-place (bank) volume of a rectangular or circular excavation, in cubic yards, cubic feet and cubic metres. Bank volume is what the surveyor measures and what a cut-and-fill balance is based on. It is not the volume that ends up in the trucks — that is larger, which is what the swell factor is for.
Vertical walls
With no side slope entered, the excavation is a box: volume = length × width × depth, taken at the base dimensions plus any working space you added on each side.
Battered walls and the prismoidal formula
When you enter a side slope ratio the excavation becomes a frustum — a box with its top opened out. The volume is calculated with the prismoidal formula, V = d/6 × (A_base + 4·A_mid + A_top), where A_mid is the area at half depth.
This matters. The common shortcut of averaging the top and base areas overstates a battered excavation, because the sides do not vary linearly in area. The prismoidal formula is exact for this shape, and for a circular pit the equivalent exact expression for a truncated cone is used.
Over-excavation and working space
Over-excavation is added to the depth before the volume is computed, so a battered excavation correctly gets wider as well as deeper. Working space is added to each side of the base dimensions, which is how the extra material at the bottom of the cut gets counted.
Swell
Swell is the percentage a material expands when it is loosened. It depends on the soil, its moisture content and how it is handled, so the field is blank by default and takes whatever figure your geotechnical report or contractor gives you. No default is supplied because there is no honest generic answer.
A 60 ft × 40 ft basement, 8 ft deep, walls battered 1.5:1
- Base length
- 60 ft
- Base width
- 40 ft
- Depth
- 8 ft
- Side slope
- 1.5 : 1
- 01A_base= 60 × 40= 2,400 sq ft
- 02A_mid= (60 + 12) × (40 + 12)= 3,744 sq ft
- 03A_top= (60 + 24) × (40 + 24)= 5,376 sq ft
- 04V = d/6 × (A_base + 4·A_mid + A_top)= 8/6 × (2,400 + 14,976 + 5,376)= 30,336 cu ft
- 05Cubic yards= 30,336 ÷ 27= 1,123.6 cu yd
1,123.6 cubic yards
What it assumes
- 01Base dimensions are measured on the floor of the excavation.
- 02Depth is uniform across the excavation and existing grade is level.
- 03Side slopes, when entered, are equal on all four sides.
- 04Swell, density and truck capacity are used only if you supply them.
What it does not do
- Sloping existing ground is not modelled. For a site that falls across the footprint, split it into sections and average the depth per section.
- Benched excavations are approximated as a uniform batter — model each bench as a separate section for a precise figure.
- Nothing here constitutes a trench safety determination. Sloping, benching and shoring requirements are set by the regulations and the competent person on your site.
Common questions.
- What is the difference between bank, loose and compacted volume?
- Bank volume is the material as it sits undisturbed in the ground — that is what this calculator returns. Loose volume is the same material after it has been dug and bulked up, which is what fills your trucks. Compacted volume is what it occupies after being placed and compacted, which is smaller again. Enter a swell factor to see the loose volume.
- Should I measure the top or the bottom of the hole?
- Enter the base dimensions and let the side slope ratio open the top out. That matches how excavations are specified — the structure sets the base size, and the batter is whatever the soil and the safety requirements demand.
- Why is the prismoidal formula better than averaging the areas?
- Because the cross-sectional area of a battered excavation changes as a quadratic with depth, not linearly. Averaging the top and base areas ignores the curvature and returns too much volume. The prismoidal formula weights the mid-depth area four times and is exact for this shape.
Behind the numbers
The methods and definitions this calculator applies, explained in full and with their sources.
Where people go next
Ordered by what usually comes next in the same job, not by keyword.