Enter the hopper height, the outlet opening size (width/diameter), and the top opening size (width/diameter) into the calculator to determine the hopper wall angle.

Hopper Angle Calculator

Rectangular Hopper Conical Hopper

Enter any 3 values to calculate the missing variable

Hopper Angle Formula

The following formula is used to calculate the hopper wall angle (measured from the horizontal) for a given hopper height, top opening width, and outlet opening width (rectangular/pyramidal hopper cross-section). For a conical hopper, use diameters instead of widths.

θ = atan(H / ((W_h - W_o) / 2))

Variables:

  • θ is the hopper wall angle in degrees, measured from the horizontal
  • H is the hopper height (vertical distance from the top opening down to the outlet plane)
  • W_h is the top opening width of the hopper
  • W_o is the outlet opening width

To calculate the hopper angle, subtract the outlet width from the top width, divide the result by 2 to get the horizontal “run” of one side, and then divide the hopper height by that run. Take the arctangent of the result. Convert the angle from radians to degrees if necessary.

What is a Hopper Angle?

The hopper wall angle is the angle formed between a hopper’s sloping wall and the horizontal plane. This angle is important in hopper design (agriculture, mining, manufacturing, etc.) because it affects how easily bulk material flows and whether it tends to bridge or rat-hole. Note: in some engineering contexts the “hopper wall angle” is reported from the vertical; if you need that convention, it is 90° − θ.

How to Calculate Hopper Angle?

The following steps outline how to calculate the Hopper Angle.

  1. First, determine the hopper height (H).
  2. Next, determine the top opening width of the hopper (W_h) (or top diameter for a conical hopper).
  3. Next, determine the outlet opening width (W_o) (or outlet diameter for a conical hopper).
  4. Finally, calculate the hopper wall angle using the formula θ = atan(H / ((W_h – W_o) / 2)).
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Hopper Height (H) = 2 m

Outlet Width (W_o) = 2 m

Top Width of Hopper (W_h) = 4 m