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Calcumetryx

Earthwork

Excavation Calculator

Cubic yards of material to be dug out — including battered side walls, over-excavation and swell.

Excavation
Start from
Excavation shape

Basements, footings, pads

Measured on the floor of the excavation, not at ground level.

Vertical distance from existing grade to the excavation floor.

Excavated volume

Excavated volume: 711.1 cubic yards. Bank measure

cubic yards

Bank measure

Section across the width, to scale
60 ft long · vertical walls
40 ft40 ft8 ftEXISTING GRADEBASE
Cubic feet
19,200cu ft
Cubic metres
543.7
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.

The working

  1. Base area = L × W

    = 60 ft × 40 ft

    = 2,400 ft²

  2. Volume = Base area × Depth

    = 2,400 ft² × 8 ft

    = 19,200 cu ft

  3. 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

Specification
Formula version
1.0.0
Last reviewed
2026-08-14
External data
None

This tool uses only your inputs and exact unit conversions. No benchmark, average or market figure is built into it. How we calculate

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.

Worked example

A 60 ft × 40 ft basement, 8 ft deep, walls battered 1.5:1

Given
Base length
60 ft
Base width
40 ft
Depth
8 ft
Side slope
1.5 : 1
Step by step
  1. A_base= 60 × 40= 2,400 sq ft
  2. A_mid= (60 + 12) × (40 + 12)= 3,744 sq ft
  3. A_top= (60 + 24) × (40 + 24)= 5,376 sq ft
  4. V = d/6 × (A_base + 4·A_mid + A_top)= 8/6 × (2,400 + 14,976 + 5,376)= 30,336 cu ft
  5. Cubic yards= 30,336 ÷ 27= 1,123.6 cu yd
Bank volume1,123.6 cubic yards
What it assumes
  • Base dimensions are measured on the floor of the excavation.
  • Depth is uniform across the excavation and existing grade is level.
  • Side slopes, when entered, are equal on all four sides.
  • Swell, 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.

Found a problem?