Earthwork Volume by Average End Area

The average end area method is the trapezoidal rule wearing a hard hat. Plot the cut or fill area of each cross section, assume the area varies linearly between them, and the solid between two stations is the mean of the end areas times the distance. It became standard because highway alignments were already being sectioned every 100 ft — one station — so the field data arrived in exactly the shape the method wants. The constant that trips people is 27: a cubic yard is 3 ft × 3 ft × 3 ft, so an answer of 15,000 ft³ is 555.6 yd³, and every North American earthwork bid is in cubic yards.

A worked example: station 12+00 sections at 120 ft² of cut, station 13+00 at 180 ft², one station apart. V = 100 × (120 + 180)/2 = 15,000 ft³ = 555.6 yd³ — about 28 truckloads at 20 yd³ each. The known bias: when the section shape changes a lot between stations the method overstates the volume, because a linear interpolation of area is a poor stand-in for the real prismoid. Agencies live with it on ordinary terrain and switch to the prismoidal formula where the money is large or the ground is a saddle.