Governing Formula
Earthwork balancing compares the volume removed by excavation with the volume required to build the finished grade. Both quantities are entered on a bank (in-situ) basis so the comparison is made on a common footing.
Net = V_cut – V_fill Where:
-
V_cut= Cut (excavated) volume of soil in its natural, in-situ state [m³] -
V_fill= Fill (embankment) volume required, expressed in the same bank state [m³] -
SW= Swell percentage: loose gain when soil is excavated and handled [%] -
SH= Shrinkage percentage: compaction loss when fill is placed and compacted [%]
Derived Equations:
Net = V_cut – V_fill V_export = (V_cut – V_fill) × (1 + SW/100) V_import = (V_fill – V_cut) × (1 + SH/100) How the Calculation Works
The calculator subtracts the fill volume from the cut volume to obtain the net balance. A positive balance means cut exceeds fill and export is required; a negative balance means fill exceeds cut and import is required.
Because soil changes volume when it moves, the haulage quantity is corrected from the bank basis: excavated soil swells (expands) when loosened, while placed fill shrinks (compacts) under rolling. The export quantity is therefore multiplied by (1 + SW/100), and the import quantity by (1 + SH/100).
Worked Engineering Example
Design Scenario: 5,000 m³ Cut against 4,000 m³ Fill (20% Swell, 10% Shrinkage)
- Net earthwork balance:
Net = 5,000 – 4,000 = +1,000 m³ (cut exceeds fill → export required) - Loose export volume (after swell):
V_export = 1,000 × (1 + 20/100) = 1,000 × 1.20 = 1,200 m³ - Compacted import volume:
Import = 0 m³ (there is no fill shortfall to import)
Engineering Notes & Design Benchmarks
| Material | Typical Swell | Typical Shrinkage |
|---|---|---|
| Common earth / loan | 20 – 30% | 8 – 15% |
| Clay (dry) | 25 – 40% | 10 – 20% |
| Gravel / sandy soil | 15 – 25% | 5 – 10% |
Swell and shrinkage are site-specific and best confirmed from a soil report and a test strip. Design typical values below 25% for swell and below 15% for shrinkage; unusually high shrinkage can occur in expansive soils.
Assumptions & Limitations
- All cut and fill volumes are entered on a bank (in-situ) basis; mixing bank and compacted volumes corrupts the balance.
- Swell and shrinkage are applied linearly as volume percentages; real behaviour depends on moisture, gradation, and compacting effort.
- The model ignores haul distances, borrow pits, and density control testing, which are separate cost considerations.
- Final determination of swell/shrinkage should be verified with compaction testing and a construction soil investigation.
Frequently Asked Questions
What is the difference between bank, loose, and compacted volume?
Bank volume is soil in its natural undisturbed state. Loose volume is the expanded state immediately after excavation (swelled). Compacted volume is the state after the fill has been placed and rolled (shrunk relative to bank). Quantities must be converted to a common basis before comparing.
What typical swell factor should I use for common earth?
Common earth and loan typically swell about 20–30% when excavated, so about 1.2–1.3 m³ of loose material is produced per 1 m³ of bank cut. Clay tends toward the higher end. Confirm the value from the geotechnical report where available.
Why is my import volume larger than the fill shortfall?
Because imported fill must be compacted from its bank delivery state. If 1,000 m³ of fill is short, you must import 1,000 × (1 + shrinkage/100) m³ to finish with the required compacted volume — the shrinkage correction covers the compaction loss during placement.
Engineering Disclaimer
Engineering Note: This calculator provides preliminary earthwork balance estimates for planning. Final cut/fill quantities, swell and shrinkage factors, and haul plans must be verified from a geotechnical investigation, compaction testing, and the construction drawings.
Technical References
- Peurifoy, R. L., Schexnayder, C. J., & Shapira, A., Construction Planning, Equipment, and Methods, McGraw-Hill.
- Nunnally, S. W., Construction Methods and Management, Pearson.
- ASTM D698: Standard Test Methods for Laboratory Compaction Characteristics of Soil Using Standard Effort, ASTM International.