Grid (borrow-pit) volume
Cut and fill over a grid of existing elevations against a finished grade: the net volume by corner weights and the four-point method, with the balance line where cut turns to fill.
Experimental: not yet fully verified. How results are checked
The net volume is 1,625 ft³: 1,714.41 ft³ of cut and 89.41 ft³ of fill by the four-point method.
| East | South |
|---|---|
| 25.000 ft | 43.750 ft |
| 50.000 ft | 30.000 ft |
| 16.667 ft | 50.000 ft |
- Cut volume (four-point)
- Fill volume (four-point)
- Net volume, cubic yards
Provenance
- Computed by
- survey.earthwork.borrow-pit 1.0.0, core 0.1.0
- Model
- Depth h = existing − proposed at each node. Net V = A/4 · Σ(w·h), w = 1 at corners, 2 on edges, 4 inside. Four-point: each cell's V = A·mean(h), or for a cell with both cut and fill, cut = A·(Σh⁺)²/(4Σ|h|) and fill = A·(Σh⁻)²/(4Σ|h|). Balance points by linear interpolation along cell edges (Ghilani & Wolf 2021, ch. 26)
- Accuracy
- Exact for the grid; the volume is as good as the grid spacing is fine against the ground's shape
- 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: Depth h = existing − proposed at each node. Net V = A/4 · Σ(w·h), w = 1 at corners, 2 on edges, 4 inside. Four-point: each cell's V = A·mean(h), or for a cell with both cut and fill, cut = A·(Σh⁺)²/(4Σ|h|) and fill = A·(Σh⁻)²/(4Σ|h|). Balance points by linear interpolation along cell edges (Ghilani & Wolf 2021, ch. 26)
Accuracy: Exact for the grid; the volume is as good as the grid spacing is fine against the ground's shape
Worked example: A 3 × 3 grid at 25 ft against a 100 ft grade. Source: add-survey-suite corner-weights scenario. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Cell size
- 25 ft
- Existing elevations
- 102.0, 101.5, 101.0 101.2, 100.6, 100.2 100.4, 99.8, 99.2
- Finished grade
- 100 ft
You get
- Net volume (corner weights)
- 1,625 ft³
- Cut volume (four-point)
- 1,714.41 ft³
- Fill volume (four-point)
- 89.41 ft³
- Net volume, cubic yards
- 60.19 yd³
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: unit-area or borrow-pit method).
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.