Calculate hopper wall angle and valley angle from height, top and outlet width, or solve the height or opening size for rectangular and conical hoppers.

Use widths in one vertical cross-section.

Valley angle
Slope of the adjacent wall pair, for the valley (corner) angle. Leave blank if all walls slope equally, as in a square hopper.

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.

ฮธ = atan(H / ((Wh - Wo) / 2))

Variables:

  • ฮธ 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)
  • Wh is the top opening width of the hopper
  • Wo is the outlet opening width

For a centered outlet and straight walls, subtract the outlet width from the top width and divide by 2 to get one sideโ€™s horizontal run. For a positive run, take atan(height/run) and convert to degrees. Equal openings give vertical walls: 90ยฐ from horizontal. For conical hoppers, use diameters.

What is a Hopper Angle?

The hopper wall angle is the angle formed between a hopperโ€™s sloping wall and the horizontal plane. This angle affects hopper geometry and material flow, but geometry alone does not establish a mass-flow design. Bulk-solid and wall-friction testing are also needed. Note: in some engineering contexts the โ€œhopper wall angleโ€ is reported from the vertical; if you need that convention, it is 90ยฐ โˆ’ ฮธ.

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 (Wh) (or top diameter for a conical hopper).
  3. Next, determine the outlet opening width (Wo) (or outlet diameter for a conical hopper).
  4. Finally, calculate the hopper wall angle using the formula ฮธ = atan(H / ((Wh - Wo) / 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 (Wo) = 2 m

Top Width of Hopper (Wh) = 4 m