Earthwork Volume Calculator: Excavation, Trench & Pile Volumes
Calculate excavation and fill volume for rectangular cuts, sloped trapezoidal trenches, and conical stockpiles in bank, loose, and compacted cubic yards. For grading projects that balance cut against fill across a site, use the cut and fill calculator instead, or pair this tool with the excavation calculator for a full material takeoff.
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Rebar Weight Chart
US Standard Rebar Sizes (#2–#18) with weight per foot, diameter, and cross-sectional area.
View Chart →Volume Formulas by Excavation Shape
Each shape uses a distinct geometric formula. Confirm which one matches your actual site condition before relying on the result for material orders.
| Shape | Formula | Typical Use | Accuracy Note |
|---|---|---|---|
| Rectangular | V = L × W × D | Footings, pads, basements | High, if walls are vertical |
| Trapezoidal Trench | V = L × D × (Wb + Wb + 2 × slope × D) / 2 | Utility trenches, sloped sides | Depends on accurate slope ratio |
| Triangular Cut | V = L × (0.5 × Wt × D) | V-ditches, swales | Assumes symmetric taper to a point |
| Conical Pile | V = (1/3) × π × r² × h | Stockpiles, spoil piles | Loose measure only, not bank |
Bank, Loose, and Compacted Volume Explained
Earthwork volume changes depending on the state of the material. Bank cubic yards (BCY) describe soil still in the ground, undisturbed. Once excavated, the same soil occupies more space as loose cubic yards (LCY) because digging introduces air voids between particles.
Compacted cubic yards (CCY) describe soil after it has been placed in a fill area and compacted with equipment. Compacted volume is usually smaller than bank volume because compaction pushes particles closer together than their natural state, a phenomenon called shrinkage.
💡 Why This Matters for Cost
A material supplier ticket quoting 100 cubic yards of fill dirt is almost always loose measure. If your geometric calculation returned 100 bank cubic yards, you may need to order roughly 125 loose cubic yards for common earth at a 25 percent swell factor to get an equivalent amount delivered.
Example Scenario: Utility Trench Excavation
A contractor needs to excavate a 100-foot-long utility trench, 6 feet deep, with a 3-foot bottom width. Local soil is classified Type B, requiring a 1:1 side slope per OSHA 29 CFR 1926.652 Appendix B.
Step 1: Determine Top Width
Bottom width: 3 ft
Slope ratio: 1:1 (1 ft horizontal per 1 ft vertical)
Depth: 6 ft
Step 2: Apply Trapezoidal Formula
Average width = (3 + 15) / 2 = 9 ft
Cross-section area = 9 × 6 = 54 sq ft
Step 3: Convert to Loose Volume
Soil type: Common earth
Swell factor: 25%
At 14 CY per truck, this trench requires 18 truck loads to haul off site.
Mistakes That Skew Earthwork Volume Estimates
Confusing Bank and Loose Measure
Entering a supplier's loose-yard delivery quantity as if it were bank volume overstates how much in-place soil is actually available, leading to under-ordering fill material.
Ignoring Side Slope Requirements
Treating a sloped trench as a simple rectangular cut understates volume significantly. A 1:1 slope on a 6-foot-deep trench adds 12 feet to the top width compared to the bottom.
Using One Swell Factor for All Soils
Applying a generic 25 percent swell factor to blasted rock, which can swell 50 to 80 percent, understates hauling volume and truck load counts by a wide margin.
Measuring Stockpiles as Bank Volume
A dumped conical stockpile is already in loose measure. Applying a swell factor a second time when comparing it to bank volume double-counts the expansion.
Using This Data for Hauling and Permits
Most local jurisdictions require a grading or excavation permit once cut or fill volume exceeds a threshold, commonly 50 to 1,000 cubic yards depending on the municipality. Check local building department requirements before starting work regardless of the volume this calculator returns.
Dump trucks are typically rated between 10 and 16 loose cubic yards for standard tri-axle configurations, though tandem trucks run smaller at 8 to 12 CY. Confirm the specific truck capacity with your hauler since it directly changes the load count in the results above.
Earthwork Volume Questions
For a rectangular excavation, multiply length by width by depth and divide by 27 to get cubic yards. For a sloped trench with side slopes, use the trapezoidal formula that averages the top and bottom widths before multiplying by length and depth.
Bank cubic yards (BCY) is soil volume measured in its natural undisturbed state before digging. Loose cubic yards (LCY) is the same soil after excavation, when it expands with air voids. A truck bed capacity is always rated in loose cubic yards.
Common earth swells approximately 25 percent after excavation, so 1 bank cubic yard becomes about 1.25 loose cubic yards. Clay swells around 30 percent, sand and gravel around 15 percent, and blasted rock can swell 50 to 80 percent depending on fragmentation size.
A conical pile volume equals one-third times pi times the radius squared times the height: V = (1/3) x pi x r^2 x h. Measure the pile's base diameter and height, then divide the result by 27 to convert cubic feet to cubic yards.
Per OSHA 29 CFR 1926.652 Appendix B, excavations deeper than 5 feet without a protective system require sloping based on soil type: 3/4 to 1 for stable rock, 1 to 1 for Type B soil, and 1.5 to 1 for Type C soil, unless a competent person approves a different configuration.
Calculated volumes are typically bank measure while delivery tickets often report loose or compacted measure. Confirm which volume basis a supplier is quoting and apply the correct swell or shrinkage factor before comparing figures.
No. This tool calculates the geometric volume of the shape entered. Topsoil stripping, typically 4 to 6 inches per local grading codes, and any required overexcavation for unsuitable soil should be added as a separate volume.
Sources and Calculation Methodology
- OSHA 29 CFR 1926.652, Appendix B — Sloping and Benching, soil classification and maximum allowable slope ratios (osha.gov).
- OSHA 29 CFR 1926 Subpart P — Excavations, general requirements for protective systems (osha.gov).
- Standard earthwork swell and shrinkage factor ranges for common earth, clay, sand/gravel, and rock, as published in general earthmoving and equipment estimating references.
- Trapezoidal prism and cone volume formulas are standard solid geometry, consistent with civil engineering earthwork estimating practice.
Verify soil classification and slope requirements with a competent person or geotechnical engineer for any excavation deeper than 5 feet.
⚠ Disclaimer
This calculator provides estimates for planning purposes. For permitted structural work, foundations, multi-story construction, retaining walls over 4 feet, and commercial projects, calculations must be verified by a licensed structural engineer per IBC 2024 §1604. ConcreteCalculate.com is not liable for structural decisions made from these estimates.
Privacy note: all calculations run in your browser and on this server per request only. No project dimensions, elevations, or contact information are stored or transmitted to a database. Built by Muhammad Ramzan Babar, physics researcher (PhD candidate). Reviewed by site author.
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