Vertical Tank with Dished Bottom calculator
Vertical cylinder with a 2:1 ellipsoidal bottom head, at any level. Exact geometry, instant results, nothing leaves your browser.
Exact segment geometry — see methodology. Dished-head propane math is documented there too.
Process vessels, brewing tanks and many poly cone-alternatives stand on a dished bottom — a 2:1 ellipsoidal head whose depth is a quarter of the diameter. The head holds less per inch than the straight shell, so gauge readings near the bottom mislead anyone using a plain-cylinder chart.
This calculator models the head exactly (affine-scaled spheroid cap — the same verified math as our propane heads, see methodology) and switches to linear shell math above the tangent line. Enter diameter and the straight-shell height; total depth is shell + D/4.
How this is calculated
V = (2/3)πr²a + πr²Hcyl, a = D/4h≤a: V = (r/a)²·πh²(3a−h)/3 | h>a: V = (2/3)πr²a + πr²(h−a)The 2:1 bottom head is a scaled spherical cap; above the tangent line it switches to linear cylinder math. See the full derivation, a worked example and a fill-ratio table on the vertical tank, 2:1 dished bottom formula page.
FAQ
TVC-112/FAQHow deep is a 2:1 dished bottom?
Exactly one quarter of the tank diameter — a 48 in tank has a 12 in head, holding 2/3·π·r²·(D/4) below the tangent line.
My tank has an F&D (shallower) bottom — does this work?
A standard ASME F&D head is shallower (0.169·D) and holds ~20% less than a 2:1; this page's 2:1 math will read slightly high in the head zone. For F&D-headed horizontal vessels use the propane calculator; an F&D vertical option is on our roadmap.
Does the head affect readings high in the tank?
No — above the tangent line every inch holds the same πr² volume; only the bottom D/4 is nonlinear.