How the volume is calculated
A standing tank is simple: the liquid fills a cylinder up to the fill level. A lying tank is harder, because the liquid surface gets wider towards the middle. The liquid forms a circular segment, which the calculator works out exactly:
Vertical: V = π · r² · h
Horizontal: A = r² · acos((r − h) ÷ r) − (r − h) · √(2rh − h²)
V = A · L
Example: A lying tank with 2 m diameter and 5 m length holds 15,708 litres. At a level of 1.2 m it contains 9,841 litres, which is 62.6 % even though the level is at 60 % of the height.
Level and volume in a horizontal tank
| Fill height (% of diameter) | Volume (% of capacity) |
|---|---|
| 10 % | 5.2 % |
| 20 % | 14.2 % |
| 30 % | 25.2 % |
| 40 % | 37.4 % |
| 50 % | 50.0 % |
| 60 % | 62.6 % |
| 70 % | 74.8 % |
| 80 % | 85.8 % |
| 90 % | 94.8 % |
This table works for any lying cylinder with flat ends, regardless of size. It is handy for making a dipstick chart.
Things to keep in mind
- Use the inside diameter. Thick walls or insulation make the outside much larger.
- Never plan to fill a tank to 100 %. Liquids expand with temperature; fuel tanks are usually limited to 90 to 95 %.
- For tanks with dished or elliptical ends, the real capacity is higher than the flat-end result.