Calculator · storage

Storage volume estimator

Calculates the geometric volume of a rectangular or cylindrical store, a cylinder with a conical peak, or a free-standing conical pile, and the mass it would hold at a bulk density you supply.

Result

Enter values to see a result.

Formula & assumptions

Volume of a rectangular prism

formula v1.0.0 · calc v1 · reviewed 2026-07-16

V = l × w × h

Applies to: Rectangular stores and containers.

Assumptions

A geometric volume of the space described. Whether a commodity can occupy all of it is a separate question.

Limitations

Geometry only — no structural, safe-working, or regulatory capacity is implied.

Scope

Not an engineering capacity. Structural limits are set by the design of the actual structure and by qualified engineers, never by multiplying three dimensions.

Sources: National Institute of Standards and Technology (NIST), U.S. Department of Commerce (opens in a new tab), Iowa State University Extension and Outreach (opens in a new tab)

Volume of a vertical cylinder

formula v1.0.0 · calc v1 · reviewed 2026-07-16

V = π × r² × h

Applies to: Cylindrical bins, silos, and tanks.

Assumptions

A right circular cylinder filled level to the stated height.
The radius is internal — an external measurement overstates the volume by the wall thickness.

Limitations

Excludes any cone, hopper, or peak above or below the cylinder — those are separate volumes.
Geometry only — no structural, safe-working, or regulatory capacity is implied.

Scope

Not an engineering capacity. Bin loading limits depend on the structure and on the commodity’s behaviour, and are an engineering determination.

Sources: National Institute of Standards and Technology (NIST), U.S. Department of Commerce (opens in a new tab), Iowa State University Extension and Outreach (opens in a new tab)

Volume of a cone

formula v1.0.0 · calc v1 · reviewed 2026-07-16

V = (1 ÷ 3) × π × r² × h

Applies to: Conical bin sections and, approximately, heaped piles.

Assumptions

A right circular cone. For a heaped pile, the height is the peak above the base, and the shape is only ever an approximation of a real pile.

Limitations

A real pile is not a cone: its slope is set by the angle of repose, which varies with commodity, moisture, and fines, and its base is rarely circular.
Geometry only — no structural, safe-working, or regulatory capacity is implied.

Scope

Not an engineering capacity, and not a basis for entering, walking on, or working around a pile — stored bulk material can engulf a person without warning.

Sources: National Institute of Standards and Technology (NIST), U.S. Department of Commerce (opens in a new tab), Iowa State University Extension and Outreach (opens in a new tab)

Volume of a cylinder with a conical peak

formula v1.0.0 · calc v1 · reviewed 2026-07-16

V = π × r² × h_cyl + (1 ÷ 3) × π × r² × h_cone

Applies to: Cylindrical bins filled above the eave.

Assumptions

A level-filled cylinder with a right circular cone of the same radius sitting on top.
The peak is an idealisation: a real heap follows the commodity’s angle of repose, which varies with moisture and fines, so the cone height is at best an estimate of a shape that is never truly conical.

Limitations

The peak’s height is not a free choice: a heap cannot be steeper than the commodity’s angle of repose, and this formula does not know or check that.
Geometry only — no structural, safe-working, or regulatory capacity is implied.

Scope

Not an engineering capacity, and not a basis for entering, walking on, or working around stored bulk material, which can engulf a person without warning. Bin loading limits are an engineering determination.

Sources: National Institute of Standards and Technology (NIST), U.S. Department of Commerce (opens in a new tab), Iowa State University Extension and Outreach (opens in a new tab)

Effective volume after a packing/void factor

formula v1.0.0 · calc v1 · reviewed 2026-07-16

V_eff = V × f ÷ 100

Applies to: Any store whose usable volume is less than its geometry.

Assumptions

The factor is the user’s own figure for the fraction of the geometric volume the commodity actually occupies — headspace, aeration ducting, access, and settling all reduce it.

Limitations

No default packing factor is supplied and none is implied. The right figure depends on the store, the commodity, the fill method, and how the space is actually used, and a generic number applied to a real store is a guess wearing a percentage.
This is not the void fraction between particles — that is already inside the bulk density. Applying both would double-count the voids.

Scope

Not an engineering capacity and not a safe working limit.

Sources: Iowa State University Extension and Outreach (opens in a new tab), Food and Agriculture Organization of the United Nations (FAO) (opens in a new tab)

Mass from volume and bulk density

formula v1.0.0 · calc v1 · reviewed 2026-07-16

m = V × ρ_bulk

Applies to: Bulk-handled commodities.

Assumptions

The bulk density supplied describes the commodity in the state it will actually occupy the space.

Limitations

Only as good as the bulk density entered. This platform does not supply a default bulk density, because a generic figure applied to a real lot is a guess wearing a number.

Scope

An arithmetic estimate, not a capacity rating. It says nothing about whether a structure can carry the resulting mass.

Sources: Food and Agriculture Organization of the United Nations (FAO) (opens in a new tab), Iowa State University Extension and Outreach (opens in a new tab)

Bulk density: kg/m³ → lb/ft³

formula v1.0.0 · calc v1 · reviewed 2026-07-16

lb/ft³ = kg/m³ × (1 ÷ 0.45359237) × 0.3048³ [exact by definition]

Applies to: Any bulk density.

Assumptions

The pound (0.45359237 kg) and the foot (0.3048 m) are exactly defined, so this factor is exact rather than measured.

Limitations

A unit conversion. It does not make a bulk density into a test weight, which is a graded measurement by a specified apparatus.

Sources: National Institute of Standards and Technology (NIST), U.S. Department of Commerce (opens in a new tab)

About this tool

Geometry only. No structural, safe-working, or regulatory capacity is implied by multiplying dimensions together.
The volume of the space described, not the quantity that can be stored in it: headspace, aeration, angle of repose, and access are not included unless you enter a packing factor for them.
The packing factor is NOT the void fraction between particles. That void space is already inside bulk density, which is mass per unit of BULK volume and so already counts the gaps. Applying a packing factor for particle voids on top of a bulk density would double-count them; the packing factor is for space the commodity does not occupy at all.
A conical peak is an idealisation. A real heap follows the commodity’s angle of repose, which varies with moisture and fines, so its shape is never truly conical.
A mass figure appears only when you supply a bulk density, and it is only ever as good as that figure.

Educational reference — not a prescription

Not an engineering certification and not a capacity rating. Structural and loading limits are set by the design of the actual structure and by qualified engineers, never by a volume calculation. Stored bulk material can also engulf a person without warning, and nothing here bears on entering or working around a store.

These calculators are for education and reference. The quality of any result depends entirely on the accuracy of the values you enter.
Local agronomic conditions, legal requirements, product labels, and professional advice may override a general calculation.
Results are not pesticide, fertilizer, irrigation, or veterinary prescriptions, and are not a substitute for advice from a qualified agronomist or your local extension service.