Volumes
 Cross Sections
 End Area Method
 Prismoidal Formula
 Rectangular Base Method
 Triangular Base Method
 Balance of Cut and Fill
 Volumes From Contours
 Digital Terrain Models

Volume Determination - The End Area Method

This is the simplest method for determining volumes from cross sections. It closely follows the theory developed for the determination of areas, in this case instead of offsets at constant separation (resulting in areas) there are areas at constant separations (resulting in volumes).

In the figure it can be assumed that areas A₁, A₂ and A₃ have been determined. Therefore, if A₁ is the left end area, A₂ the right end area and d the separation between sections, the first volume is,

V = d

Now consider several successive cross sections situated at equal distances, d, along a fixed direction. Then,

V = d(A₁ + A₂)/2 + d(A₂ + A₃)/2 + d(A₃ + A₄)/2 + ........ + d(A_n-1 + A_n)/2

V = d[A₁ + 2A₂ + 2A₃ + 2A₄ + ......... + 2A_n-1 + A_n]/2

V = [First area + last area + 2S(all remaining areas)]

This End Area formula may be applied to any number of cross sections equally spaced along a straight line.