Last reviewed 16 Sept 2026 · 7 min read
Earthwork computation
Data
- Longitudinal section (L-section) — ground levels (RL) at regular chainages (e.g. every 20 m or 30 m) along the centre line, with the proposed formation level (road/canal bed) fixed by gradient.
- Cross-sections — ground levels across the centre line at each chainage.
- Formation width, side slopes (cutting and filling), road/canal typical sections.
Depth at a section:
- Embankment (filling): height formation level ground level (positive).
- Cutting: depth ground level formation level.
Sectional area of a level section
FormulaLevel section (ground level across the section)
= formation width (top width of embankment or bottom width of cutting); = depth of fill or cut at the centre line; = side slope (horizontal : 1 vertical).
Volume between sections
FormulaEarthwork volume formulas (sections at distance L apart)
1. Mid-section (mean depth) method:
2. Mean sectional area (trapezoidal / average end area) method:
For a series of equally spaced sections:
3. Prismoidal formula:
( = area at the mid-section.) For a series with an odd number of equally spaced sections:
- For level sections, the mean area method gives a slightly larger volume than the prismoidal formula (difference = prismoidal correction ); the mid-section method gives a slightly smaller volume.
- The prismoidal formula is the most accurate for regular sections.
Mixed sections and transitions
- Where the formation changes from embankment to cutting, the section at the transition point has zero depth; the chainage of the transition point is found by interpolation between adjoining sections of fill and cut.
- Side-long (partly cut, partly fill) sections on sloping ground are computed as triangles/trapezoids for the cut and fill portions separately.
Lead and lift
- Lead — horizontal distance over which excavated earth is carried, measured between the centres of gravity of excavation and deposit (or as specified).
- Lift — vertical height through which earth is raised.
- Schedule rates commonly include an initial lead of 50 m and lift of 1.5 m; extra lead and lift are paid additionally. Lifts may be converted to equivalent leads as per departmental rules.
Mass haul diagram
A plot of cumulative volume of earthwork (cuts positive, fills negative, corrected for shrinkage/bulking) along chainage, used to decide economic haul, borrow pits and spoil, free haul and overhaul (see Computation of Areas & Volumes).