Vertical Tank Volume
Fill volume of a vertical cylindrical tank from the level.
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The engineering
The easy orientation: volume is linear in level, so percent full equals percent of height and every centimetre of level is worth the same number of litres (that conversion is its own result row — handy for sizing level alarms and drip legs). The assumption is a flat bottom; cone-bottom or dished-bottom tanks need the bottom section handled separately.
The L/cm row is also the leak-math row: a 3 m diameter tank holds about 71 L per centimetre, so a level drop of a millimetre overnight is 7 litres gone — measurable with a decent gauge, invisible on a sight glass.
Where this math comes from
Cylindrical storage is as old as cisterns and granaries, and its arithmetic — circle times height — has been correct since Archimedes measured the cylinder around 250 BCE (he was proud enough of the sphere-in-cylinder result to put it on his tomb).
What the modern era added is scale and standards: welded steel verticals for oil (API 12C in 1936, consolidated into API 650 in 1961) and water, with strapping tables, floating roofs, and level instrumentation making the simple formula into a custody instrument. Vertical tanks dominate tank farms precisely because their linear level-to-volume law makes inventory honest.
- 250 BCEArchimedesVolume of the cylinder — the formula, permanently (circa).
- 1936API12C welded tank standard — steel verticals standardized.
- 1961APIAPI 650 — the modern welded storage-tank standard.
See the full timeline of the math behind every calculator →
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