KEVOS® MAKEOS · Materials
Stockpile Volume and Weight from Angle of Repose
How much material is in a natural pile on this circular or rectangular base?
Volume and weight of bulk material piled naturally to its angle of repose on a circular base (a cone) or a rectangular base (a ridged pile with sloping ends), from the base size, the angle of repose and the bulk density.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Base | choice | Shape of the base the pile stands on. |
| Base diameter (circular) | m | Diameter of the circular base. |
| Base width, shorter side (rectangular) | m | Shorter side of the rectangular base. |
| Base length, longer side (rectangular) | m | Longer side of the rectangular base. |
| Angle of repose | ° | Natural angle of repose of the material (from material data or measurement). |
| Bulk density | kg/m³ | Bulk (loose) density of the material. |
Method and formulas
- Cone: h = (D ÷ 2) tan θ; V = π D² h ÷ 12. This is the handbook’s W = M D³ with M = ρ π tan θ ÷ 24.
- Rectangular: h = (A ÷ 2) tan θ; V = A h (3B − A) ÷ 6 (a ridged pile sloping on all four sides).
- Weight = V × bulk density.
- Example: a 3 m circular base at 35° holds about 3.9596 t.
Limitations
- Dry, loose material that flows to its natural angle; moist, cohesive or compacted material differs.
- Density varies with compaction and moisture: use upper and lower values for limits.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate the weight of a stockpile on a floor or plate
- Check floor or plate loading under a pile
- Size a storage area for a quantity of bulk material
Who it is for
- Process engineers
- Site and yard supervisors
- Estimators
What you get
- Pile height
- Volume
- Weight and average base pressure
Interpreting the result
- Run the calculation with high and low densities to bracket the weight, as the handbook does.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 382–383. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
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