Excavation calculator with slopes, cut and fill
This excavation calculator works out how much soil comes out of a foundation pit or trench — with sloped or vertical sides — and how much cut and fill a site needs, either from a grid of spot levels or from cross-sections along a road or channel. It then turns the in-place volume into the loose volume that has to be carted away, the number of truckloads, the weight in tonnes or US tons, and the compacted volume if the soil goes back in as fill.
Contractors use it to price earthwork, engineering students to check grid-method and average-end-area problems, and home builders to see how many tipper loads a basement or septic pit will make. Soil presets supply typical swell and compaction factors and in-place densities for common earth, clay, sand, gravel and blasted rock, and every factor can be changed to your soil report.
All calculations run in your browser. The results are estimates for planning; levels should come from a proper survey and earthwork contracts from your engineer’s quantities.
How to use the Excavation Calculator
- Choose metric or imperial, then what you are digging: a pit, a trench, a grid of levels or a set of cross-sections.
- For a pit or trench, enter the bottom size, depth and side slope (0 for vertical sides, 1 for 1 horizontal to 1 vertical). For a grid, enter the spacing, the design level and the ground levels row by row. For sections, enter each chainage with its cut and fill area.
- Pick the soil type or enter your own density, swell factor and compaction factor.
- Set the truck load (loose) and, if you like, an excavation rate per bank m³ or yd³.
- Read the bank volume, loose volume, weight, truckloads and, for cut and fill, the surplus or shortfall. Copy the summary for your estimate.
Excavation Calculator features
Sloped excavations
Pits use the prismoidal formula, which is exact for straight sloping sides; trenches use the trapezoid cross-section.
Grid cut and fill
Each grid square is split into two triangles and cut and fill are integrated separately, so cells that cross the design level are handled correctly. A colour map shows cut and fill at every point.
Cross-sections
Average end area method for roads, embankments, canals and drains.
Swell and compaction
Bank, loose and compacted volumes, with surplus to haul away or soil to import.
Tons and truckloads
Weight from in-place density and truck count from the loose volume.
Formulas used
- Pit with sloped sides: top length = L + 2sd and top width = W + 2sd, where s is the slope (horizontal per vertical) and d the depth. Volume = d ÷ 6 × (A₁ + 4Aₘ + A₂) — the prismoidal formula with the bottom, mid-depth and top areas. Example: a 4 × 3 m pit 2 m deep at 1:1 has a top of 8 × 7 m and holds 62.67 m³.
- Trench: volume = length × depth × (bottom width + top width) ÷ 2. A 10 m trench 0.6 m wide and 1.2 m deep with 0.5:1 sides is 14.4 m³.
- Grid method: each square of the level grid is divided into two triangles; within a triangle the ground is taken as a plane, and the parts above and below the design level are calculated exactly.
- Average end area: volume between two sections = distance × (A₁ + A₂) ÷ 2. It slightly overestimates when the sections differ greatly in shape.
- Loose volume = bank volume × swell factor; compacted volume = bank volume × compaction factor; weight = bank volume × in-place density.
Swell and compaction factors by soil
Swell and compaction factors are from the US Army field manual FM 5-434, Earthmoving Operations (2000), Table 1-1; densities are bank (in-place) values from Caterpillar’s published earthwork tables. Sources differ — Caterpillar gives about 22% swell for clay in its natural bed against 43% in FM 5-434 — so use figures from your own soil investigation when you have them.
| Soil | Bank → loose (swell) | Bank → compacted | In-place density |
|---|---|---|---|
| Sand or gravel | 1.11 | 0.95 | 1.60 t/m³ (sand) · 2.17 t/m³ (pit-run gravel) |
| Loam / common earth | 1.25 | 0.90 | 1.90 t/m³ |
| Clay | 1.43 | 0.90 | 2.02 t/m³ |
| Rock, blasted | 1.50 | 1.30 | ≈ 2.67 t/m³ |
Practical tips
- Slopes: cuts deeper than about 1.5 m (5 ft) in soil normally need sloping, benching or shoring for safety. Follow your local regulations (for example OSHA 1926 Subpart P in the US) and the engineer’s design.
- Working space: add 300–600 mm (1–2 ft) around footings for formwork and access before calculating the pit.
- Truckloads are counted on loose volume: a 6 m³ tipper carries less than 5 m³ of the hole when the soil swells 25%.
- Need to bring stone in afterwards? Use the gravel calculator. Digging for a septic tank? Size it first with the septic tank size calculator.
Excavation Calculator FAQ
How do I calculate excavation with a slope?
Work out the top dimensions by adding twice the slope × depth to the bottom length and width, then use the prismoidal formula: volume = depth ÷ 6 × (bottom area + 4 × mid-depth area + top area). The excavation calculator does this when you enter a side slope.
How do I convert excavation volume to tons?
Multiply the bank (in-place) volume by the soil density. 50 m³ of common earth at about 1.9 t/m³ weighs roughly 95 tonnes. Use the in-place density, not the loose one, with the bank volume.
What is a cut and fill calculation?
It compares existing ground levels with the design level. Ground above the design level is cut, ground below is fill. This calculator does it from a grid of spot levels or from cross-section areas and tells you whether soil must be hauled away or brought in.
What is the swell factor of soil?
The ratio of loose to in-place volume after digging. Common earth swells about 25% (factor 1.25), clay 30–45%, sand and gravel 10–15% and blasted rock about 50%.
How many truckloads will my excavation make?
Multiply the bank volume by the swell factor and divide by the truck’s loose capacity, rounding up. 62.7 m³ of earth × 1.25 = 78.3 m³ loose, which is 14 loads in a 6 m³ tipper.
Why is the fill shortfall bigger than the fill volume difference?
Compacted fill is denser than soil in its natural state (factor 0.90 for earth), so each cubic metre of fill needs about 1.11 m³ of bank soil.