Volume of a Rectangular Hopper Formula

Given here is the volume of a rectangular hopper formula to calculate the volume of the rectangular based tapered hopper. For the volume calculation, first measure the upper rectangular dimensions and the lower rectangular dimensions. The units of measurement must remain consistent throughout the entire process. Measure the height through center from the upper base to the lower base. Now, substitute all the values for the variables in the formula for the Rectangular Based Tapered Hopper Volume calculation.


V = (H / 3) [(X2Y - x2y) / (X - x)]


V = Volume
H = Height between Bases
X = Length of Upper Rectangular Base
Y = Width of Upper Rectangular Base
x = Length of Lower Rectangular Base
y = Width of Lower Rectangular Base

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The gravity inside the tapered hopper causes the material inside the hopper to feed out the bottom when opened. The formula for the volume of a tapered hopper is based on the volume of a geometric pyramid or cone. The volume for a pyramid with any base is found by multiplying the area of the base by the height and dividing by 3.

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