How cut and fill is calculated
Three methods, one idea: measure how far the ground is from where it needs to be, everywhere, and add it up — keeping the cut and the fill apart the whole way.
Last updated 3 September 2026
Four numbers, not one
- Cut: the in-place volume where existing ground is above proposed grade. It comes out.
- Fill: the in-place volume where existing ground is below proposed grade. It goes in.
- Net: cut minus fill. Positive is export, negative is import. It sizes the trucking off site.
- Total moved: cut plus fill. It sizes the machine time, and it is what gets priced.
The grid method
Lay a square grid over the site. At each intersection, subtract the proposed elevation from the existing one: positive means the ground must come down (cut), negative means it must come up (fill). Then, for each cell:
Cell volume
Cell volume = (d₁ + d₂ + d₃ + d₄) ÷ 4 × Cell area
The four corner depths averaged, times the cell’s plan area. A positive result is cut, a negative one is fill. The averaging assumes the surfaces vary linearly across the cell, which is what a finer grid makes true.
Here is the calculator’s own preset worked by hand: a 25 ft grid — cell area 625 sq ft — with nine depths in feet, north row first: 2, 2, 2 / 0.5, 0.5, 0.5 / -1, -1, -1.
| Cell | Corner depths (ft) | Average | Volume | Which |
|---|---|---|---|---|
| NW | +2, +2, +0.5, +0.5 | +1.25 ft | 781 cu ft = 28.9 cu yd | Cut |
| NE | +2, +2, +0.5, +0.5 | +1.25 ft | 781 cu ft = 28.9 cu yd | Cut |
| SW | +0.5, +0.5, -1, -1 | -0.25 ft | 156 cu ft = 5.8 cu yd | Fill |
| SE | +0.5, +0.5, -1, -1 | -0.25 ft | 156 cu ft = 5.8 cu yd | Fill |
| Result | Volume |
|---|---|
| Cut | 57.9 cu yd |
| Fill | 11.6 cu yd |
| Net | 46.3 cu yd export |
| Total moved | 69.4 cu yd |
Nine points is a teaching grid. A real site uses hundreds, on a tighter spacing, and the arithmetic is identical — which is why this is what estimating software does underneath, and why you can check its output on any one cell by hand.
Why area × average depth fails
Average the nine depths above and multiply by the site area and you get 46.3 cu yd — the net, and nothing else. It cannot say how much of that is cut, how much is fill, or how much has to be handled. Change the site to one that rises 1 ft along the north row and falls 1 ft along the south and the failure is total:
| Method | Says |
|---|---|
| Area × average depth | 0 cu yd — nothing to do |
| Grid method | Cut 23.1 cu yd, fill 23.1 cu yd, net 0, moved 46.3 cu yd |
Both are arithmetically correct about the net. Only one of them is a quantity anyone can price.
Cross-sections: average end area and the prismoidal formula
For long, narrow work — roads, channels, embankments — the site is cut into slices at regular stations along its length. At each station the cross-section is drawn and its cut and fill areas measured. The volume between two stations is then estimated from the two end areas.
Average end area
V = (A₁ + A₂) ÷ 2 × L
The two end areas averaged, times the distance between them. Exact when the section changes linearly along the length; it overstates the volume when the section tapers, because the true shape between two areas is a prismoid, not a wedge.
Prismoidal formula
V = L ÷ 6 × (A₁ + 4 × Aₘ + A₂)
Adds a measured mid-section Aₘ. It is exact for any section whose area varies as a quadratic along the length — which covers most earthwork — and it is the correction applied when the end-area figure matters.
With end areas of 120 and 80 sq ft 50 ft apart, and a mid-section measured at 98 sq ft — example inputs — the average end area gives 185.2 cu yd and the prismoidal formula 182.7 cu yd. The difference is small here; on a long taper it is not.
What software does
Estimating software builds a triangulated surface from every survey point of the existing ground, another from the design, and computes the volume between them one triangular prism at a time — the grid method with cells shaped to the data instead of to a ruler. Its accuracy is set by how densely the ground was surveyed, not by the method; a sparse survey through a fine algorithm is still a sparse survey.
Swell and shrink change the balance
Every volume above is in place — bank measure. Cut material bulks up once dug, and fill material takes more loose material than its finished volume once compacted. Whether the cut actually covers the fill is therefore a question in loose measure:
Loose from cut
Loose from cut = Cut × (1 + Swell)
Swell for the material being dug.
Loose needed for fill
Loose needed = Fill × (1 + Shrinkage)
Shrinkage is a separate figure from swell, for the material being placed and the compaction it gets. See the bank vs loose guide.
A site with equal cut and fill in bank measure is not balanced once both factors are applied, and it can go either way. The factors come from the soil report — this site ships none.
How Calcumetryx handles it
The cut and fill calculator is the grid method above, with nine spot depths and four cells, and it shows every cell. It reports cut, fill, net and total moved separately, warns when a small net hides a large total, and applies swell and shrinkage only if you enter them. The excavation calculator handles a single prism when the whole area is cut; the fill dirt calculator handles the compacted side.
Sources
- Grid, average-end-area and prismoidal volumes are defined by the formulas above — Arithmetic — verifiable by handSupports: Every figure and table on this page. The grid example is the calculator’s preset, recomputed here from the same nine depths. · checked 3 September 2026
Put it to work
All earthwork calculators →The grid method with every cell shown, and the tools for the volumes on either side of it.