About the Hopper Valley Angle Calculator
This tool finds the slope angle of the valley line where two flat hopper side panels intersect. It is useful for hopper layout, fabrication checks, and understanding how side slopes combine at rectangular or non-square plan corners.
How to use this calculator
- Choose whether the panel angles are measured from horizontal or vertical.
- Enter the Side 1 angle in degrees.
- Enter the Side 2 angle in degrees.
- Enter the plan angle between the two side slope directions, using 90° for a square corner.
- Click Calculate Valley Angle to view the valley slope and related geometry.
- Click Reset to restore the default 60°, 60°, and 90° inputs.
How it works
The calculator treats each hopper side as a flat plane and calculates the slope of the line where those two planes intersect. If the input angles are measured from vertical, they are first converted to angles above horizontal by subtracting each value from 90°.
For each side, the calculator uses the tangent of the panel slope to describe the plane steepness. It then combines the cotangents of the two panel slopes with the plan angle between them to find the horizontal run per 1 unit of vertical drop.
The valley angle is calculated as the arctangent of 1 divided by that horizontal run per drop. The result is reported as degrees above horizontal, along with drop per horizontal unit, run per drop, panel-to-panel inside angle, and the valley direction in plan.
This is an educational geometry tool only. Final hopper fabrication angles should be verified with project drawings, material flow requirements, and a qualified designer.
Example calculation
Suppose both hopper panels are 60° above horizontal and meet at a 90° plan corner. The cotangent of 60° is about 0.577, so the horizontal run per 1 unit drop is sqrt(0.577² + 0.577²) = 0.816. The valley slope angle is atan(1 / 0.816), which gives approximately 50.77° above horizontal.
Frequently asked questions
What does the valley angle mean in a hopper?
It is the slope angle of the intersection line where two sloped hopper panels meet, measured above horizontal.
Should I enter hopper angles from horizontal or vertical?
Use the selector to match your drawing. If the drawing shows angles from vertical, choose Vertical so the calculator can convert them to slopes above horizontal.
What plan angle should I use for a rectangular hopper corner?
Use 90° when the two side slope directions meet at a square corner in plan view.
Why is the valley angle lower than the side panel angles?
The valley line runs diagonally between the two sloped planes, so it usually has a flatter slope than either individual panel.
Can this be used for final fabrication dimensions?
Use it as an educational estimate only. Final fabrication geometry should be checked against the project design and by a qualified professional.