A 20 m by 20 m building pad worked on a 10 m grid produces 72.5 m³ of bank cut and 62.5 m³ of compacted fill. A driveway takeoff on two cross-sections 40 ft apart produces 44.44 yd³ of bank cut and 8.89 yd³ of compacted fill. Every step that produces those numbers is checkable, and every volume carries its state label.
All dimensions, depths, areas, factors, and results are stated example fixtures verified by independent calculation. They demonstrate the arithmetic and describe no real site.
What site does this example use?
The metric part of the example grades a 20 m by 20 m pad, staked on a 10 m grid with four 100 m² cells. At each grid point the surveyor records the existing elevation and the proposed elevation; the depth is existing minus proposed. Positive depth is cut, negative depth is fill, and a zero reading sits exactly on the proposed surface.
The grid readings keep the cut/fill boundary on a grid line, so no cell mixes cut and fill corners. That keeps this walkthrough clean. A cell that straddles the boundary needs its cut and fill portions separated before its volume is computed, as the cut-and-fill volume methods page explains.
| Row | x = 0 m | x = 10 m | x = 20 m |
|---|---|---|---|
| y = 20 m | -0.5 | -0.7 | -0.6 |
| y = 10 m | 0.0 | 0.0 | 0.0 |
| y = 0 m | 0.6 | 0.8 | 0.7 |
How do the four cells add up?
Cell volume is the mean of its four corner depths multiplied by the cell area. Take each cell's corners, average them, multiply by 100 m², and label the result cut or fill.
Cell volume = (depth&sub1; + depth&sub2; + depth&sub3; + depth&sub4;) ÷ 4 × cell area
| Cell | Corner depths (m) | Mean depth (m) | Volume |
|---|---|---|---|
| A (x 0 to 10, y 0 to 10) | 0.6, 0.8, 0.0, 0.0 | 1.4 ÷ 4 = 0.350 | 35.0 m³ cut |
| B (x 10 to 20, y 0 to 10) | 0.8, 0.7, 0.0, 0.0 | 1.5 ÷ 4 = 0.375 | 37.5 m³ cut |
| C (x 0 to 10, y 10 to 20) | 0.0, 0.0, -0.5, -0.7 | -1.2 ÷ 4 = -0.300 | 30.0 m³ fill |
| D (x 10 to 20, y 10 to 20) | 0.0, 0.0, -0.7, -0.6 | -1.3 ÷ 4 = -0.325 | 32.5 m³ fill |
Total cut = 35.0 + 37.5 = 72.5 m³, measured in place before digging. That is the bank volume. Total fill = 30.0 + 32.5 = 62.5 m³, measured as finished grade after placement. That is the compacted volume. Compare them without converting states and the balance reads 72.5 − 62.5 = 10.0 m³ of bank soil to export.
Cut leaves the ground in its bank state; fill arrives as a compacted target. The bank vs loose volume guide shows why volumes measured in different states never subtract directly.
What changes when the fill must be compacted?
Compacted fill takes more bank soil than its finished volume. Convert the fill target back to the bank state with a shrink factor from the project record or an approved reference. With an example-only factor of 1.20:
Bank soil needed for fill = 62.5 m³ compacted × 1.20 = 75.0 m³ bank
The site holds 72.5 m³ of bank cut, so the true balance is 72.5 − 75.0 = −2.5 m³. The naive 10.0 m³ export has flipped into a 2.5 m³ bank import. Compaction changed the hauling decision, which is exactly why the cut-and-fill ordering guide applies the factor before booking trucks.
Shrinkage depends on the soil, the moisture, the equipment, and the specified density. Use a factor measured on your material or taken from a reference your project accepts, and keep the factor and its source in the record.
How does the same check work with cross-sections?
A driveway takeoff uses two cross-sections 40 ft apart. Each section shows a cut area and a fill area; the average-end-area method extends them into volumes.
Volume = (area at section 1 + area at section 2) ÷ 2 × distance
| Quantity | Section 1 | Section 2 | Volume |
|---|---|---|---|
| Cut | 36 ft² | 24 ft² | (36 + 24) ÷ 2 × 40 = 1,200 ft³ = 44.44 yd³ bank |
| Fill | 0 ft² | 12 ft² | (0 + 12) ÷ 2 × 40 = 240 ft³ = 8.89 yd³ compacted |
With the same example-only 1.20 factor, the compacted fill needs 8.89 × 1.20 = 10.67 yd³ of bank soil. The export is 44.44 − 10.67 = 33.77 yd³ bank. The field procedure that feeds this calculation is covered in how to measure a site for cut and fill.
How do you know the answer is sane?
Run four checks before the quantity leaves the site.
First, each cell mean must sit between zero and its largest corner depth; here 0.350, 0.375, −0.300, and −0.325 all pass against corner maxima of 0.8 and −0.7. Second, the site-wide mean depth should look like the readings: 72.5 m³ over 400 m² is 0.18 m, comfortably inside the recorded depths. Third, confirm the balance direction against the terrain: more ground above proposed grade than below it means a cut-dominant site, which matches the surplus. Fourth, re-add the cells and verify the unit conversions: 1,200 ÷ 27 = 44.44 and 240 ÷ 27 = 8.89. When a check fails, suspect the readings or the arithmetic before the method.
Safety and professional scope
Volume arithmetic does not select excavation slopes, shoring, protective systems, haul routes, or legal truck payloads. Payment quantities follow the contract measurement provision, and the project specification controls accepted survey practice and tolerances.
Cut faces and placed fill are ground-work hazards: keep clear of unsupported faces, control water that can change soil strength, and verify protective systems against the excavation plan. Quantity planning does not replace drawings, specifications, permits, or a qualified professional.
Sources and scope
- Wyoming DOT, Survey Manual, Appendix F: average-end-area and zero-end/pyramidal volume methods for earthwork cross-sections.
- FHWA, Earthwork Representation Guide (Central Federal Lands): grid, section, and surface representations of earthwork quantities.
- Caltrans, Construction Manual, Section 4-19 Earthwork: field verification of planned ground surfaces and terrain changes before relying on survey quantities.
- NIST Handbook 44, 2026 Appendix C: cubic-foot, cubic-yard, and cubic-metre relationships used in the worked conversions.
Scope: the dimensions, depths, areas, factors, and results in this article are stated fixtures verified by independent calculation; they demonstrate the arithmetic and describe no real site. Survey-grade volumes, payment acceptance, material-specific swell and shrinkage values, and accepted tolerance bands are outside this page. Contract measurement provisions, safety rules, and acceptance requirements remain project-specific.
Review responsibility: Saleem Sial owns the published calculation, source, and editorial checks. Waseem Sial, External Reviewer and Engineer, remains listed for ongoing external review; no completed external-review date is claimed.
Next, use the Cut and Fill Calculator to work out the section volumes, then study the full method comparison on the cut-and-fill volume methods page, or return to the Earthwork & Drainage Calculators hub.
