Earthwork volume from survey points: grid, TIN and cross sections

Updated: 2026-08-04 · ISKRIT

Given a set of surveyed points and a reference surface, three established methods produce a volume. They agree on flat ground and diverge exactly where the money is: on broken terrain and at the edges of the survey.

Grid of squares

The site is covered with a regular grid, a level is interpolated at each node, and each cell contributes the average of its corner working heights times its area. It is the method that hand calculation was built around, it produces a drawing anyone can check, and it is still what many acceptance procedures expect to see.

Its weakness is the cell that straddles the zero line, where cut turns into fill. Averaging four corners of mixed sign underestimates both quantities. The correct treatment splits the cell along the zero line and integrates the two parts separately, which is arithmetic no one wants to do by hand and every calculator should do automatically.

Triangulated surface

A Delaunay triangulation over the surveyed points reproduces the surface without inventing a grid, and the volume is the sum of prism volumes under each triangle. Nothing is interpolated that was not measured, which makes it the honest method when the survey is irregular, dense in places and sparse in others.

The subtlety is numerical rather than conceptual. Long thin triangles at the survey boundary, a 190 m base with a one centimetre bulge, have circumscribed circles hundreds of kilometres across, and the in-circle test that builds the triangulation loses its meaning in double precision. Exact geometric predicates are the fix, and without them a survey with nearly collinear boundary points produces a triangulation whose areas do not sum to the site area.

Cross sections

Volume is computed between successive profiles, each section area times the distance to the next, by the average end area rule or the prismoidal formula. It is the natural method for linear works, roads, channels, trenches, and it is weak on wide sites, where the choice of section spacing quietly determines the answer.

Where they disagree

On a smooth surface all three land within a percent of each other. On broken ground the grid method is the least accurate at cell size above a few metres, cross sections depend entirely on spacing, and triangulation tracks the measured points. When a claim turns on a volume, the method and its parameters, cell size or section interval, matter as much as the survey itself, and both belong in the report.

Questions

Which method should acceptance use? Whichever the contract names; if it names none, the grid method produces the drawing that is easiest to argue from.

Does bulking belong in these numbers? No. These are in-situ volumes; the bulking factor is applied afterwards, when the haulage is counted.

Load surveyed points and get cut and fill by triangulation, with a grid cartogram and a DXF drawing, in the earthwork volumes tool.