OpenSpecEngineering

Finds the volume of earth to cut or fill between two cross-sections of a road, channel, embankment or site grading plan by the average end area method [1]. Surveyors, estimators and civil engineers use it to total earthwork station by station along a corridor, for cost estimates, haul planning and pay quantities.

Equation

V = L·(A₁ + A₂) / 2

A₁ and A₂ are the end areas: the area of cut (or of fill) on each cross-section, measured between the existing ground line and the design template. L is the distance between the two sections along the centerline, usually the difference of their stations. The result is the volume of the slice between them, in cubic meters and in cubic yards (27 ft³). For a whole job, run each pair of neighboring sections and add the slices.

Limits and common mistakes

• Keep cut and fill apart. A section can have both, on opposite sides of the centerline. Find the cut volume from the cut areas and the fill volume from the fill areas, never from their net.
• The method assumes the area changes evenly between the sections. Where the shape changes sharply, it usually overstates the volume; the prismoidal formula, which also needs the middle area, is more exact [1]. Closer sections reduce the error.
• Where cut runs out to zero (a transition from cut to fill), the slice is closer to a pyramid, V = A·L/3, and the average end area overstates it by 50 %. Add a section at the zero point.
• The result is a bank (in-place) volume. Soil swells when dug and shrinks when compacted, so cut and fill volumes don’t balance one for one. Apply shrink and swell factors before matching cut to fill or ordering trucks.
• On a curve, the centerline distance is right only when each area is centered on the centerline; otherwise correct for the offset of its centroid.

Worked example

A road cut has an end area of 245 ft² at station 12+00 and 310 ft² at station 13+00. How many cubic yards of excavation lie between them?

1. Set the unit of Cross-Section Area 1 to ft² and enter 245.
2. Set the unit of Cross-Section Area 2 to ft² and enter 310.
3. Set the unit of Distance Between Sections to ft, enter 100 and press Solve. The Solution shows: Volume: 785.792 m³
   Volume: 1,027.78 yd³

Check by hand. The average area is (245 + 310) / 2 = 277.5 ft², so the slice is 277.5 × 100 = 27,750 ft³, and 27,750 / 27 = 1,027.8 yd³. A handy shortcut for 100 ft stations: the volume in cubic yards is the sum of the two areas in ft² times 1.852 (100 / 54).