Calculator Inputs
This version models a rectangular straight-wall bin above a rectangular hopper frustum. Enter top dimensions larger than outlet dimensions.
Example Data Table
| Scenario | Top Size | Outlet Size | Heights | Fill | Density | Usable Volume | Total Mass |
|---|---|---|---|---|---|---|---|
| Aggregate feed hopper | 4.5 m × 3.2 m | 1.0 m × 0.8 m | 1.6 m straight + 2.4 m hopper | 90% fill, 95% usable | 1600 kg/m³ | 64.84 m³ for 2 hoppers | 103.74 t total |
Formula Used
The calculator combines a straight-wall storage box with a lower rectangular frustum.
1. Top and outlet areas
Atop = Top Length × Top Width
Aoutlet = Outlet Length × Outlet Width
2. Straight wall volume
Vstraight = Atop × Straight Wall Height
3. Hopper frustum volume
Vhopper = h ÷ 3 × (Atop + Aoutlet + √(Atop × Aoutlet))
Here, h is the hopper section height.
4. Gross, filled, and usable capacity
Gross Volume = Vstraight + Vhopper
Filled Volume = Gross Volume × Fill Level
Usable Volume = Filled Volume × Usable Capacity Factor
5. Material mass and truck trips
Material Mass = Usable Volume × Bulk Density
Truck Trips = Total Material Mass ÷ Truck Payload
How to Use This Calculator
Step 1: Select metric or imperial units.
Step 2: Enter top opening dimensions for the bin.
Step 3: Enter outlet dimensions for the discharge opening.
Step 4: Enter straight wall and hopper section heights.
Step 5: Add fill percentage and usable capacity factor.
Step 6: Enter material bulk density and hopper count.
Step 7: Add optional truck payload for haulage planning.
Step 8: Press calculate and review the chart, totals, and export options.
Frequently Asked Questions
1. What hopper shape does this calculator use?
It models a rectangular storage section above a rectangular frustum hopper. This setup fits many aggregate, batching, and materials handling applications on construction projects.
2. Why does usable volume differ from gross volume?
Gross volume is the full geometric space. Usable volume accounts for fill limits and dead zones. That adjustment better reflects practical working capacity on site.
3. What bulk density should I enter?
Use the in-place bulk density for the stored material. Common examples include sand, gravel, crushed stone, cement, or recycled aggregate. Field-tested values give better results.
4. Can I use imperial dimensions?
Yes. Switch the unit system to imperial. The calculator converts feet, pounds per cubic foot, and short tons into consistent internal values automatically.
5. What does the usable capacity factor represent?
It represents the percentage of filled volume that is realistically available. Bridging, buildup, freeboard, and operating practice can reduce practical capacity below geometric capacity.
6. Why are outlet dimensions important?
Outlet dimensions influence hopper geometry and discharge design. A larger outlet changes frustum volume and can affect the balance between storage capacity and material flow performance.
7. What does the truck trips result show?
It estimates how many truckloads are needed for the total stored material. The result helps with dispatch planning, delivery sequencing, and temporary stockyard logistics.
8. Is this suitable for detailed fabrication design?
No. It is a planning and estimation tool. Detailed structural, discharge, liner, and fabrication design should still be checked by the responsible engineer.