BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Base
- What it is
- The shape of the ground the pile covers: a circle, which gives a cone, or a rectangle, which gives a ridged pile sloping on all four sides.
- Units and format
- Choose one of 2 options from the list: Circular (cone); Rectangular (ridged pile).
- Example
- The form opens with “Circular (cone)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Circular uses the base diameter; rectangular uses the two sides.
What this means: Base diameter (circular)
- What it is
- The diameter of the circular base of a cone-shaped pile, measured across the toe of the pile on the ground.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 1000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Volume and weight rise with the cube of the base diameter.
- Get it right
- Measure at the toe where the pile meets the ground; this is a diameter, not a radius.
What this means: Base width, shorter side (rectangular)
- What it is
- The shorter side of a rectangular base, which sets the height of the ridge for a given angle of repose.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 1000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be the shorter side; the tool refuses a width larger than the length.
What this means: Base length, longer side (rectangular)
- What it is
- The longer side of a rectangular base, along which the ridge of the pile runs.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 1000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure along the toe of the pile on the ground.
What this means: Angle of repose
- What it is
- The natural angle of repose of the material: the steepest slope, from the horizontal, at which a loose pile of it stands without sliding.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 5° to 70°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pile height and volume are proportional to the tangent of this angle.
- Get it right
- Take it from material data or measure a free-poured pile; moisture changes it.
What this means: Bulk density
- What it is
- The bulk density of the loose material, the mass of a volume including the air between the particles.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1600 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The weight is directly proportional to the bulk density.
- Get it right
- Use loose bulk density, not the solid density of the material; test it or ask the supplier.
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.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Angle of repose, heaps and avalanches
In Bulk Solids Flow by the Numbers
What it covers: What the angle of repose measures, why heaps grow and fail in avalanches of every size, how the heap in a silo costs capacity and fools level sensors, and why repose is not a hopper angle.
BIZOMAT 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.
Open the Stockpile Volume and Weight from Angle of Repose calculator