Level Measurement · Free Calculator
Cone Bottom Tank and Silo Volume Calculator
Calculate the volume at any level in a vertical cylindrical tank or silo with a conical bottom, and the mass stored for a given density.
Conical bottomSilos and hoppersVolume and massStrapping table
Volume21.206 m³
Mass21.206 t
Percent of volume54.55 %
Cone volume3.534 m³
Total volume38.877 m³
How this result was calculated
- Cone: V = π r² h ÷ 3 with r = R × h ÷ hcone
- Above the cone: add π R² × (h − hcone)
- V = 21.206 m³
Level to volume strapping table
| Level % | Level | Volume | Volume % |
|---|---|---|---|
| 0 % | 0 m | 0 m³ | 0.0 % |
| 10 % | 0.65 m | 0.28759 m³ | 0.7 % |
| 20 % | 1.3 m | 2.3007 m³ | 5.9 % |
| 30 % | 1.95 m | 6.7152 m³ | 17.3 % |
| 40 % | 2.6 m | 11.31 m³ | 29.1 % |
| 50 % | 3.25 m | 15.904 m³ | 40.9 % |
| 60 % | 3.9 m | 20.499 m³ | 52.7 % |
| 70 % | 4.55 m | 25.093 m³ | 64.5 % |
| 80 % | 5.2 m | 29.688 m³ | 76.4 % |
| 90 % | 5.85 m | 34.283 m³ | 88.2 % |
| 100 % | 6.5 m | 38.877 m³ | 100.0 % |
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Cone and Cylinder Volume
Cone part (h ≤ hc): V = π × (R h/hc)² × h ÷ 3
Above: V = π R² hc ÷ 3 + π R² (h − hc)
Above: V = π R² hc ÷ 3 + π R² (h − hc)
Worked example
A 3 m silo with a 1.5 m cone and 5 m cylinder filled to 4 m from the tip holds 3.53 + 17.67 = 21.21 m³.
Key insight: for bulk solids the surface is not flat: material forms a cone at its angle of repose when filling and a funnel when emptying. Point level and weighing often give a better inventory than a single level reading.
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Frequently Asked Questions
How do I calculate a cone bottom tank volume?
Add the cone volume (π R² h/3) and the cylinder volume above it (π R² × height of liquid in the cylinder).
Is level measured from the cone tip or the cylinder?
This calculator measures level from the cone tip. Add the cone height if your sensor references the cylinder.
Can I use this for powders?
Yes, with bulk density, but note that the surface angle of solids adds uncertainty.
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