Bin and Hopper Volume Calculator
A round bin or silo is modelled as two stacked shapes: a straight cylinder for the vertical wall and a truncated cone (frustum) for the tapered hopper below it.
Enter Values
How to use this calculator
- Enter the top (bin) diameter and, if there is a vertical wall above the hopper, the straight-wall height.
- Enter the hopper (cone) height and the outlet diameter — leave the outlet at blank/zero for a hopper that comes to a point.
- Press Calculate to read the total volume in m³ and capacity in litres.
How it works
A round bin or silo is modelled as two stacked shapes: a straight cylinder for the vertical wall and a truncated cone (frustum) for the tapered hopper below it. The cylinder volume is π × R² × h, where R is the bin radius. The hopper is a conical frustum with volume (π × h ÷ 3) × (R² + R·r + r²), where R is the top radius and r is the outlet radius; when the outlet is zero this reduces to the ordinary cone volume (π × h × R²) ÷ 3.
The two volumes are added to give the total. Capacity in litres is simply the total cubic metres multiplied by 1000 (1 m³ = 1000 L). All inputs are in metres and the calculation is exact geometry, so the answer is the geometric volume — usable free-flowing capacity is a little less once you allow for the angle of repose of the stored material and any freeboard left at the top.
Worked example
3 m bin with a 4 m wall and a 2 m hopper. A round bin 3 m across with a 4 m straight wall sits on a conical hopper 2 m tall tapering to a 0.5 m outlet. The straight section holds π × 1.5² × 4 = 28.27 m³ and the hopper adds (π × 2 ÷ 3) × (1.5² + 1.5×0.25 + 0.25²) = 5.63 m³, for a total of 33.9 m³ — a capacity of 33,903 L.
Common mistakes
- Entering a radius where a diameter is asked for (or vice versa) — every field on this tool is a diameter, so a 3 m bin uses 3, not 1.5.
- Treating a flat-bottomed bin as having a hopper: if the base is flat, set the hopper height to zero and use only the straight-wall height.
- Forgetting freeboard and angle of repose — the geometric volume is the brim-full shape; real usable storage of grain or granules is somewhat less.
Frequently asked questions
What shape does this calculator assume?
A round bin: an optional vertical cylinder wall on top of a conical hopper that tapers to a round outlet. Set the straight-wall height to zero for a plain hopper cone, or set the hopper height to zero for a flat-bottomed cylindrical bin.
How is the hopper volume worked out?
The hopper is a truncated cone (frustum) with volume (π × h ÷ 3) × (R² + R·r + r²), where R is the top radius, r is the outlet radius and h is the hopper height. If the outlet diameter is left blank the outlet radius is zero and the formula becomes the standard cone volume.
Is the answer the amount of grain I can actually store?
No — it is the exact geometric (brim-full) volume of the shape. Real usable capacity for grain or granules is a little smaller once you allow for freeboard at the top and the angle of repose of the material.
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Tip: Enter any known values to calculate the remaining results.
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