If h₁ and h₂ are the difference in levels between the ground surface and the formation levels at the two sections and ‘n’ is the side slope and ‘D’ is the distance between them, the prismoidal correction for a level section is  

Explanation:

The volume of earthwork by trapezoidal method  = V1

V1 =  \(common\: distance\left \{ \frac{First\: area + Last\: area}{2}+the \:sum \:of\: remaining \:area \right \}\)

The volume of earthwork by prismoidal formula = V2

V2 = \(=\frac{Common\: distance}{3}\left \{ First\: area+ Last\: area + 2(Sum\: of odd\: area) + 4(Sum\: of even\: area)\right \}\)

Prismoidal correction:

• The volume by the prismoidal formula is more accurate than any other method
• But the trapezoidal method is more often used for calculating the volume of earthwork in the field.
• The difference between the volume computed by the trapezoidal formula and the prismoidal formula is known as a prismoidal correction.
• Since the trapezoidal formula always overestimates the volume, the prismoidal correction is always subtractive in nature is usually more than calculated by the prismoidal formula, therefore the prismoidal correction is generally subtractive.
• Volume by prismoidal formula = volume by the trapezoidal formula - prismoidal correction

Prismoidal correction (CP)

\(C_{P}=\frac{- DS}{6}\left \{ d- d_{1}\right \}^{2}\)

Where, D = Distance between the sections, S (Horizontal) : 1 (Vertical) = Side slope, d and d1 are the depth of earthwork at the centerline