Spike's Calculators

Truncated Rectangle Hopper Volume

Truncated Rectangle Hopper Volume Calculator

Calculate the volume of a truncated hopper. It also calculates the valley angle of this hopper.

where H is the height
A the area of the inlet side
B the outlet area
one cubic inch (in³) = 0.016387064 litres (L)
one cubic inch (in³) = 0.000578703703703704 cubic feet (ft³)
Example Calculation
inlet-A length = 24 inches
inlet-B width = 9 inches
outlet-a = 4 inches
outlet-b = 4 inches
height-H = 20 inches

First, calculate the area of the inlet and the outlet;
24 * 9 = 216
Inlet-A has an area of 216 square inches.

4 * 4 = 16
Outlet-B has an area of 16 square inches.

Plug the values into the formula;
20 ÷ 3 * ( 216 + 16 + √216 * 16)
6.666666666666667 * (216 + 16 + 58.78775) 
6.666666666666667 * 290.78775 = 1938.585
This hopper has a volume of 1938.585 cubic inches.

Note: the calculation is unitless. We use inches, but you can use any length unit as long as they are the same. The calculator uses inches, and the conversions to cubic feet and litres are from using inches for the length measurements. It goes without saying that for this calculator to work correctly, the outlet has to be smaller than the inlet side.

Truncated Rectangle Hopper Volume

Inlet Length/Side A in
Inlet Width/Side B in
Outlet Length/Side a in
Outlet Width/Side b in
Hopper Height in


Hopper Volume in³
Volume in Cubic Feet ft³
Volume in Litres L
Angle c °
Angle d °
Valley Angle °


  1. inlet length A
  2. inlet width B
  3. outlet length a
  4. outlet length b
  5. the height


  1. hopper volume in cubic inches
  2. in cubic feet
  3. in litres
  4. angle c located on side A
  5. angle d located on side B
  6. the valley angle
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