Tank volume and level.
Calculate total and liquid volume for a vertical or horizontal cylindrical tank with flat, 2:1 semi-elliptical or hemispherical heads, with a level-to-volume table.
Results
Preliminary estimate for early engineering. Check against your design basis, standards and vendor data.
Method
Level-to-volume table
| Level, m | Level, % | Volume, m³ | Volume, % of total |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0.25 | 10 | 1.647 | 4.9 |
| 0.5 | 20 | 4.619 | 13.8 |
| 0.75 | 30 | 8.315 | 24.8 |
| 1 | 40 | 12.441 | 37.1 |
| 1.25 | 50 | 16.772 | 50 |
| 1.5 | 60 | 21.102 | 62.9 |
| 1.75 | 70 | 25.228 | 75.2 |
| 2 | 80 | 28.924 | 86.2 |
| 2.25 | 90 | 31.896 | 95.1 |
| 2.5 | 100 | 33.543 | 100 |
How it is calculated
Heads are treated as half-ellipsoids of revolution with depth 0 (flat), D/4 (2:1 semi-elliptical) or D/2 (hemispherical). For a horizontal tank, the shell holds a circular segment of area:
A(h) = R² cos⁻¹((R − h) / R) − (R − h) √(2Rh − h²)
and the two heads together form an ellipsoid whose partial volume is a sphere cap scaled by the head depth. For a vertical tank, each head’s partial volume comes from integrating the ellipsoid cross-section, with the straight shell in between. Total volume is πR²L plus (4/3)πR²c for the pair of heads, where c is the head depth.
Real tanks differ slightly: torispherical heads, nozzles, internals and plate thickness all change the volume. Use certified strapping tables for custody transfer.
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Calculated with the free engineering tools at nicuzn.com/tools. Preliminary estimate for early engineering; check against your design basis, applicable standards and vendor data before use.