Stockpile volume (TIN)
A stockpile's volume from its base outline and surface shots: a Delaunay measured above the plane fitted to the base, in cubic units and cubic yards.
Experimental: not yet fully verified. How results are checked
The stockpile holds 8,333.33 ft³, or 308.64 yd³.
- Volume, cubic yards
- Base area
- Triangles
- Highest point above the base
Provenance
- Computed by
- survey.earthwork.stockpile 1.0.0, core 0.1.0
- Model
- Delaunay TIN (Bowyer–Watson) over the base vertices and surface shots; base plane z = a + bx + cy by least squares through the base vertices; volume = Σ triangle area × mean height above the plane, over triangles inside the outline (Ghilani & Wolf 2021, ch. 26)
- Accuracy
- Exact for the TIN; a real pile's volume depends on how densely its surface was shot, especially along ridges and breaks
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Delaunay TIN (Bowyer–Watson) over the base vertices and surface shots; base plane z = a + bx + cy by least squares through the base vertices; volume = Σ triangle area × mean height above the plane, over triangles inside the outline (Ghilani & Wolf 2021, ch. 26)
Accuracy: Exact for the TIN; a real pile's volume depends on how densely its surface was shot, especially along ridges and breaks
Worked example: A pile on a 50 ft square base, peaking 10 ft up. Source: A square pyramid: base area × height / 3 = 8,333.33 ft³. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Base outline
- 0 ft, 0 ft, 100 ft 50 ft, 0 ft, 100 ft 50 ft, 50 ft, 100 ft 0 ft, 50 ft, 100 ft
- Surface shots
- 25 ft, 25 ft, 110 ft
You get
- Volume
- 8,333.33 ft³
- Volume, cubic yards
- 308.64 yd³
- Base area
- 2,500 ft²
- Triangles
- 4
- Highest point above the base
- 10 ft
Review: Not yet independently reviewed by a licensed surveyor.
Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Changes
- 2026-09-23, fixed: Survey tools cite Ghilani and Wolf's Elementary Surveying, 16th edition (2021), but their method notes said "Ghilani & Wolf 2018". The notes now give 2021, the edition cited. No results change. Changelog
Checked against: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapter 26 (volumes: TIN-based volumes and volumes of solids).
Terms
- TIN: triangulated irregular network
- A surface built by joining surveyed points into triangles, each flat, so the ground between shots is taken as varying linearly. Volumes and contours are computed from those triangles. Source: Elementary Surveying: An Introduction to Geomatics
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.
TIN — triangulated irregular network
A surface built by joining surveyed points into triangles, each flat, so the ground between shots is taken as varying linearly. Volumes and contours are computed from those triangles.
Source: Elementary Surveying: An Introduction to Geomatics