Conical Stockpile Volume Calculator

Estimate the volume of a conical stockpile from its base diameter and angle of repose.

For a free-standing cone, volume = ⅓ × π × r² × h, where height h = r × tan(angle of repose). A 20 m base at 37° holds about 789 m³.

Calculator

Base diameter (m)Angle of repose (°)Typical: dry sand ≈ 34°, crushed rock ≈ 37–40°, coal ≈ 38°.

Stockpile volume

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How it works

A heaped pile of loose material forms a cone whose slope equals the material's angle of repose. The radius is half the base diameter, the height comes from the angle, and the cone volume formula does the rest.

Worked example

Diameter 20 m → radius 10 m. Height = 10 × tan(37°) = 7.54 m. Volume = ⅓ × π × 10² × 7.54 ≈ 789 m³.

Assumptions & limitations

Assumes a clean, symmetrical cone on flat ground with a uniform angle of repose. Multiply by bulk density to get tonnes. For survey-grade figures use a drone/photogrammetry volume — this is a quick field estimate.

Frequently asked questions

What angle of repose should I use?

It depends on the material and moisture: dry sand is around 34°, crushed rock 37–40°, and coal about 38°. If unsure, measure the slope of an existing pile or use 37° as a working default for crushed rock.

How do I convert volume to tonnes?

Multiply the volume by the loose bulk density (t/m³) of the material. For example 789 m³ of crushed rock at 1.6 t/m³ is about 1,262 tonnes.

Is this accurate enough for reconciliation?

It's a quick estimate that assumes a perfect cone. For inventory reconciliation or sales, use a surveyed or drone-photogrammetry volume, which captures the real, irregular shape.

Last updated 21 June 2026

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