Tank Volume Calculator
Total and filled volume for cylindrical, rectangular and spherical tanks.
How it works
A vertical tank is easy — volume rises linearly with level, so a dipstick is a straight scale. Every other shape is not, and the horizontal cylinder is the one that catches everyone.
For a horizontal cylinder, the wetted cross-section is a circular segment:
V = L × [r² arccos((r − h) ÷ r) − (r − h)√(2rh − h²)]
The consequence is that a horizontal tank half full by depth is exactly half full by volume — that much is intuitive — but a tank filled to a quarter of its diameter holds only about 20% of its capacity, not 25%. A dipstick calibrated linearly on a horizontal tank is wrong everywhere except the middle, and wrong in the direction that makes you think you have more fuel than you do.
Spheres are worse still: a spherical cap at a quarter depth holds about 16% of the sphere. Cone-bottom tanks are the mildest case, since a cone's volume is a third of the cylinder that contains it, but the transition where the level crosses from cone to cylinder puts a visible kink in the level-to-volume curve.
None of this includes the fittings. A real tank has a dished head, a manway, an outlet standpipe and a heel of unusable liquid below it, so the working capacity is always somewhat less than the geometric one.
Common questions
Why isn't my horizontal tank half full at half depth?
It is — that is the one point where the linear guess is right, because the circle is symmetric about its centre. Everywhere else it is wrong: at a quarter of the diameter you have about 20% of the volume, not 25%.
How do I make a dipstick?
Work out the volume at a series of depths and mark those, rather than dividing the stick evenly. For a horizontal cylinder the marks bunch up near the top and bottom and spread out through the middle.
Does this account for dished ends?
No — it treats the ends as flat. A real pressure vessel with dished heads holds more, typically 2–5% more for a shallow dish and up to 10% for hemispherical ends. For a rough allowance, add the head volume from the manufacturer's data.
What is the mass figure for?
It assumes water at 1 kg per litre, which is the quick check for whether the floor or the frame can carry it. A full 2 m by 3 m vertical tank is around 9.4 tonnes — worth knowing before it goes on a mezzanine.