Drawing № TVC-115 · Dished heads

Dished head tank volume calculator

Horizontal pressure vessels and storage tanks with 2:1 elliptical or ASME flanged-and-dished heads. Pick the head type, enter the inside diameter, the shell length and a dipstick reading.

FIG. 1 — TANK CROSS-SECTION · LIVE

SCALE AUTO · REV A

01 · Tank shape

02 · Dimensions

Dim. unit

Liquid

03 · Fill depth (dipstick)50%

Wetted depth—

Surface width—

Ullage—

Liquid volume at fill depth

—US gal

Total capacity—

Filled · liters—

Filled · ft³—

Percent full—

Liquid weight—

Remaining to full—

Exact segment geometry — see methodology. Dished-head propane math is documented there too.

What to measure

D = inside diameter. Lcyl = length of the straight shell between the tangent lines. Each 2:1 head is a quarter of the diameter deep: a = D ÷ 4. h = liquid depth, measured from the lowest point inside the tank.

2:1 elliptical or F&D?

Look at the depth of the head from the seam to the centre of the end. A 2:1 elliptical head is about a quarter of the diameter deep and evenly rounded. An ASME F&D head is flatter — a shallow dish with a sharp turn (the knuckle) at the edge. Same diameter and shell length, the elliptical-head vessel holds more: on a 48 in × 120 in shell, 1,065.4 gal against 1,017.5 gal, where the shell alone is 940.0 gal.

2:1 elliptical heads — total

V = πr²·L + (2/3)πr²·a, a = D/4

2:1 elliptical heads — at liquid depth h

V(h) = seg(r,h)·L + ½·πh²(3r−h)/3

ASME F&D heads — at liquid depth h

V(h) ≈ seg(r,h)·L + (0.1545·D/r)·πh²(3r−h)/3

The elliptical-head term is exact: the head pair is a sphere squashed along the tank axis, and squashing scales every partial volume by the same ratio. The F&D term is a calibrated approximation. At an 18 in dipstick reading the 48 in example holds 361.6 gal with 2:1 heads and 346.5 gal with F&D heads. Derivations: 2:1 ellipsoidal heads and ASME F&D heads.

Head volume by diameter

Add two heads to the shell volume (π × r² × L ÷ 231) for a full-tank figure, or use the table to check a fabricator's capacity.

Volume of one head, by inside diameter
Diameter	2:1 elliptical head	ASME F&D head	2:1 head depth (D/4)
24 in	7.8 gal	4.8 gal	6.00 in
30 in	15.3 gal	9.5 gal	7.50 in
36 in	26.4 gal	16.3 gal	9.00 in
42 in	42.0 gal	25.9 gal	10.50 in
48 in	62.7 gal	38.7 gal	12.00 in
60 in	122.4 gal	75.6 gal	15.00 in
72 in	211.5 gal	130.7 gal	18.00 in
84 in	335.9 gal	207.6 gal	21.00 in
96 in	501.3 gal	309.8 gal	24.00 in
120 in	979.2 gal	605.1 gal	30.00 in

Hemispherical ends? Use the capsule tank calculator. Residential propane tanks, sized by water capacity and the 80 % rule: propane tank volume. Upright tank with a dished bottom: dished bottom tank.

FAQ

TVC-115/FAQ

What is the difference between a 2:1 elliptical head and an F&D head?

A 2:1 elliptical (semi-ellipsoidal) head is half an ellipse turned about the tank axis, a quarter of the diameter deep. A flanged-and-dished (torispherical) head is a shallow spherical dish joined to the shell by a tight knuckle; the common ASME F&D head has a dish radius equal to the diameter and a knuckle radius of 6 % of it. The 2:1 head is deeper, so it holds more.

Which length do I enter?

The straight length between the two head-to-shell seams — tangent line to tangent line. The short straight flange on each head is cylindrical and belongs in that length. If you only know the overall length, subtract the two head depths: D ÷ 4 each for 2:1 heads.

How do I calculate the volume of a 2:1 elliptical head?

One 2:1 head holds π × D³ ÷ 24 cubic inches, about 0.1309 × D³; divide by 231 for US gallons. A 48 in head holds 62.7 gal. The pair together is half a sphere of the same diameter.

How accurate is the F&D figure?

The true flanged-and-dished profile has no tidy closed formula, so the calculator scales a spherical cap to match the standard 0.0809 × D³ head volume. Checked against numerical integration of the real profile, the worst error is 0.8 % of the head-pair volume — the test is on the methodology page.

Does it handle 80/10 or shallow-dished heads?

No. Only 2:1 elliptical and standard ASME F&D (100 % dish, 6 % knuckle) heads are modelled. For other head profiles, take the head volume from the head manufacturer's data and add it to the shell volume.

Sources and standards

ASME Boiler and Pressure Vessel Code, Section VIII, Division 1 — paragraph UG-32, formed headsAmerican Society of Mechanical EngineersPaid standard — cited by designation; obtain from the publisher.Defines ellipsoidal (2:1) and torispherical heads; cited for the head definitions only — the volumes here are computed geometry.
Methodology — partial-fill formulas, head approximations and their tested errortankvolumecalc.comhttps://tankvolumecalc.com/methodology/
Handbook 44, Appendix C — General Tables of Units of MeasurementNational Institute of Standards and Technology, U.S. Department of Commercehttps://www.nist.gov/document/2026-nist-handbook-44-appendix-cUS gallon = 231 in³ exactly; Imperial gallon = 4.54609 L.

Every linked source above was retrieved and checked on 2026-11-01.