Level Measurement · Free Calculator
Spherical Tank Volume Calculator
Calculate liquid volume in a spherical tank (such as an LPG sphere) at any level, with a strapping table for transmitter characterisation.
SpherePartial volumeStrapping tableLPG storage
Liquid volume113.1 m³
Percent of volume21.60 %
Percent of level30.00 %
Total volume523.6 m³
How this result was calculated
- V = π × h² × (3R − h) ÷ 3 = 113.1 m³
Level to volume strapping table
| Level % | Level | Volume | Volume % |
|---|---|---|---|
| 0 % | 0 m | 0 m³ | 0.0 % |
| 10 % | 1 m | 14.661 m³ | 2.8 % |
| 20 % | 2 m | 54.454 m³ | 10.4 % |
| 30 % | 3 m | 113.1 m³ | 21.6 % |
| 40 % | 4 m | 184.31 m³ | 35.2 % |
| 50 % | 5 m | 261.8 m³ | 50.0 % |
| 60 % | 6 m | 339.29 m³ | 64.8 % |
| 70 % | 7 m | 410.5 m³ | 78.4 % |
| 80 % | 8 m | 469.14 m³ | 89.6 % |
| 90 % | 9 m | 508.94 m³ | 97.2 % |
| 100 % | 10 m | 523.6 m³ | 100.0 % |
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Spherical Cap Volume
V = π × h² × (3R − h) ÷ 3
Total = π × D³ ÷ 6
Total = π × D³ ÷ 6
Worked example
A 10 m sphere filled to 3 m holds π × 9 × (15 − 3) ÷ 3 = 113.1 m³, only 21.6 % of its 523.6 m³ capacity at 30 % level.
Key insight: volume changes slowly near the top and bottom of a sphere and fastest at the middle. Configure a strapping curve in the level transmitter or DCS so operators see true volume.
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Frequently Asked Questions
How do I calculate the volume of a partly filled sphere?
Use the spherical cap formula V = πh²(3R − h)/3, where h is the liquid depth and R the radius.
What is the volume at 50 % level?
Exactly half, because a sphere is symmetrical about its middle.
Does this include nozzles and internals?
No. For custody transfer use a calibrated strapping table from tank calibration.
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