Advanced Hopper Capacity Calculator

Calculator inputs

Use internal dimensions for the most direct capacity result.

Server + live preview

1. Geometry selection

Hopper shape

Dimension unit

Dimension basis

Top length

Top width

Top diameter

Straight-wall height

Hopper-section height

Overall height

Used to derive a missing section height.

Outlet length

Outlet width

Outlet diameter

Wall thickness

Internal liner thickness

Number of outlets

2. Wall slope and flow geometry

Wall angle

Angle reference

Automatic height

Calculate hopper height from angle

Angle of repose

Characteristic particle size

Entered in millimeters.

Material flowability

Outlet offset

Rounded-corner allowance

Percentage of gross volume.

Internal structures deduction

Percentage for braces, inserts, and internals.

Agitator volume

Uses the selected output-volume unit.

3. Capacity allowances

Maximum fill percentage

Freeboard percentage

Reserve percentage

Dead-space percentage

Capacity safety factor

4. Material and density

Material preset

Density condition

Density unit

Bulk density

Loose density

Compacted density

Moisture percentage

Moisture correction factor

Packing factor

Aeration factor

5. Level and sensor calculations

Material level reference

Selected material level

Low-level sensor

High-level sensor

6. Filling, discharge, and batches

Discharge rate

Discharge-rate unit

Fill rate

Fill-rate unit

Batch size

Entered in kilograms.

Material consumption

Entered in kilograms per hour.

7. Output and report settings

Preferred volume unit

Preferred mass unit

Decimal precision

Scientific notation

Use for extreme values

Project name

Project reference

Notes

Live estimate

Approximate client-side preview before submission.

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Gross capacity

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Working capacity

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Corrected density

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Wall angle

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Saved presets

Formula used

Rectangular straight section

V = L × W × H

The straight bin section uses a rectangular-prism formula.

Cylindrical straight section

V = πr²H

The cylindrical section uses its circular cross-sectional area.

Conical frustum

V = (πH / 3)(R² + Rr + r²)

This supports a full cone when the outlet radius equals zero.

Rectangular pyramidal frustum

V = (H / 3)(A₁ + A₂ + √(A₁A₂))

A₁ is the top area. A₂ is the outlet area.

Usable working volume

Vw = Vnet × Fill% − Reserve − Dead space

Optional deductions are applied before operational allowances.

Stored material mass

M = Vw × ρcorrected

Density correction includes moisture, packing, and aeration factors.

How to use this calculator

Select the hopper shape that best represents the vessel.
Choose a dimension unit and identify dimensions as internal or external.
Enter the top, outlet, straight-wall, and sloped-section dimensions.
Choose a material preset or enter a measured bulk density.
Add fill, freeboard, reserve, dead-space, and safety allowances.
Enter sensor levels, flow rates, and batch information when needed.
Review the live estimate, then calculate for the full server result.
Download a CSV or PDF report for records and engineering review.

Engineering guidance

Gross capacity versus working capacity

Gross capacity is the volume enclosed by the entered geometry. Net capacity subtracts corner, liner, agitator, and internal-structure allowances. Working capacity then applies operating fill, reserve, dead-space, and safety settings.

Bulk density selection

Bulk density changes with moisture, compaction, particle distribution, aeration, and handling history. Use measured project data whenever possible. Preset values are only starting points.

Hopper flow limitations

Capacity equations do not predict reliable discharge. Mass-flow design requires wall-friction data, cohesive-strength testing, outlet sizing, feeder interaction, and structural review. The bridging and ratholing messages are preliminary advisories only.

Level calculations

The level table integrates the changing hopper cross-section from the outlet upward. Once material reaches the straight section, volume increases linearly with height.

Common mistakes

Frequent errors include using external dimensions without thickness deductions, applying solid density instead of bulk density, ignoring freeboard, and treating nominal outlet size as guaranteed flow capacity.

Frequently asked questions

Can this calculator handle a full cone?

Yes. Select the conical frustum option and enter an outlet diameter of zero.

Should I enter internal or external dimensions?

Internal dimensions provide the most direct volume. External dimensions are reduced using the entered wall and liner thicknesses.

Why is working capacity lower than geometric capacity?

Working capacity applies fill limits, freeboard, reserve, dead-space, equipment deductions, and the selected safety factor.

Does the outlet guidance guarantee flow?

No. It is a particle-size screening check. Cohesive materials require material testing and professional hopper design.

How is capacity between sensors calculated?

The calculator evaluates volume at both sensor elevations and subtracts the lower volume from the upper volume.

Can density presets replace measured values?

No. Presets are representative. Actual bulk density can differ significantly with moisture, packing, aeration, and particle grading.

How is discharge time estimated?

Stored mass is divided by the converted mass discharge rate. Real discharge may vary with feeder control and flow behavior.

Is this a structural design tool?

No. It estimates storage and operational quantities. Structural stresses, pressures, supports, welds, and code compliance need qualified engineering analysis.