How do you calculate the volume of a horizontal cylindrical tank?

Total volume is the cylinder, π D² L / 4, plus the volume of both heads. The liquid volume at level h is the shell length L times the circular segment area R² cos⁻¹((R − h)/R) − (R − h)√(2Rh − h²), plus the liquid in each head.

What is the volume of a 2:1 ellipsoidal head?

A 2:1 ellipsoidal head has a depth of D/4 and holds π D³ / 24, about 0.1309 D³. In a horizontal tank filled to level h, one head holds π a h² (3R − h) / (6R), where a is the head depth and R the radius.

What is the volume of an ASME F&D head?

An ASME flanged and dished (torispherical) head with crown radius equal to D and knuckle radius 6% of D is about 0.169 D deep and holds about 0.0810 D³.

What is a tank strapping table?

A strapping table, or tank calibration chart, lists the liquid volume for each level increment. Operators dip or gauge the level and read the volume from the table. This calculator generates one for any vessel and exports it as CSV.

Should I use the inside or outside diameter for tank volume?

Use the inside diameter. Using the outside diameter overstates the volume by roughly four times the wall thickness divided by the diameter: about 1% for a 96 in tank with a 1/4 in wall.

KasperCalc: Tank Volume Calculator for Horizontal & Vertical Vessels

Partial Volume of Horizontal & Vertical Vessels

Orientation

Horizontal

Vertical

Ellipse ratio D/(2·depth)

Dimensions & Liquid

Inside diameter, Din

Straight length, L (T/T)in

Liquid

Known

Liquid level, hin

–

Vessel (to scale)

Results

Liquid volume—

Percent full (by volume)—

Liquid level, h—

Total vessel volume—

Empty space (ullage)—

Volume of each head—

Cylinder (shell) volume—

Head depth—

Overall inside length—L + 2 × head depth

Inside surface area—Shell + both heads

Wetted surface area—Below the liquid level

Liquid weight—Needs specific gravity

Status

Graphs & Strapping Table

The slope of this curve is the liquid surface area. A horizontal tank's curve is steepest at half full, where the surface is widest.

For a horizontal tank, 25% of the diameter is only about 20% of the shell volume. Never read a horizontal tank's level as percent full.

Level increment in

Also called a tank calibration chart or gauge table. Level is measured from the vessel bottom. Increment is the volume added since the row above.

Volumes come from integrating the exact head profile, so they agree with the closed-form results for ellipsoidal, hemispherical and conical heads. Inside dimensions only; nozzles, internals, manways and wall thickness are not included.

Real heads have a short straight flange before the tangent line. Include it in L if you measure from weld seams.

Reference Guide: Tank & Vessel Volume

Vessel Dimensions

Horizontal tank with ellipsoidal heads, showing inside diameter D, straight length L between tangent lines, head depth and liquid level h from the bottom. — Horizontal Vessel

Vertical tank with ellipsoidal heads, showing inside diameter D, straight length L between tangent lines, head depth and liquid level h from the bottom of the bottom head. — Vertical Vessel

A pressure vessel or process tank is a cylindrical shell closed by a head at each end. The tangent line is where the straight shell stops and the curve of the head starts. Vessel drawings give the shell length tangent to tangent (T/T), which is the L this calculator uses.

Total volume\[ V_{total} = \frac{\pi D^2}{4}\,L + 2\,V_{head} \]

Vessel Head Types

Six vessel heads drawn to scale on the same diameter: 2:1 ellipsoidal, hemispherical, ASME F&D, 80:10 torispherical, 30 degree conical and flat, with each head's depth as a fraction of D. — Heads Drawn to Scale

Using the table: multiply by the diameter cubed (volume), squared (area) or as is (depth). A 2:1 head on a 96 in vessel holds 0.1309 × 96³ = 115,800 in³, which is 501 US gal, and is 24 in deep.

Head	Depth	Volume	Inside area
2:1 Ellipsoidal	0.250 D	0.1309 D³	1.084 D²
Hemispherical	0.500 D	0.2618 D³	1.571 D²
ASME F&D (f = 1, k = 0.06)	0.169 D	0.0810 D³	0.931 D²
80:10 (f = 0.8, k = 0.1)	0.226 D	0.1099 D³	1.015 D²
Conical, 30° half-angle	0.866 D	0.2267 D³	1.571 D²
Conical, 45° half-angle	0.500 D	0.1309 D³	1.111 D²
Flat	0	0	0.785 D²

Per head, using inside diameter D. Computed by this calculator.

2:1 ellipsoidal: the most common head on pressure vessels. Depth is a quarter of the diameter.
Hemispherical: strongest for its thickness, so used at high pressure. Deepest and most expensive to form.
F&D and 80:10: torispherical heads. Shallow and cheap, common on low-pressure tanks.
Conical: hoppers and bottoms that must drain solids or slurries completely.

Torispherical (F&D) Head Geometry

Right half of a torispherical head. A spherical crown of radius f times D is joined to the cylinder by a toroidal knuckle of radius k times D. — Crown and Knuckle

A torispherical head is set by two radii, both written as fractions of the diameter: the crown (dish) radius \(f\,D\) and the knuckle radius \(k\,D\).

Head depth\[ c = \sqrt{(fD - kD)^2 - \left(\tfrac{D}{2} - kD\right)^2} \qquad depth = fD - c \]

\(c\) is the distance from the tangent line down to the centre of the crown sphere. The knuckle meets the crown at a height \(c\,k/(f - k)\) above the tangent line.

Inside or outside? ASME F&D heads are usually specified with the crown radius equal to the outside diameter. This calculator uses inside dimensions for both radii, which is very close for thin walls. For exact work, enter the inside crown and knuckle radii as fractions of the inside diameter.

Partial Volume of a Horizontal Tank

Left: a circle filled to level h, showing the circular segment of liquid. Right: a head cut into thin vertical slices, each a smaller circle with the same liquid surface. — Segment and Slices

The Shell

Every cross-section of the shell holds the same circular segment of liquid, so the shell's liquid volume is the segment area times L:

Circular segment, R = D/2\[ A(h) = R^2 \cos^{-1}\!\left(\frac{R-h}{R}\right) - (R-h)\sqrt{2Rh - h^2} \]

\[ V_{shell}(h) = L\,A(h) \]

The Heads

A head's slices get smaller toward the apex, but the liquid surface stays at the same height. For an ellipsoidal head of depth \(a\) (including hemispherical, \(a = R\)), the result has a closed form:

One ellipsoidal head\[ V_{head}(h) = \frac{\pi\,a\,h^2\,(3R - h)}{6R} \]

Torispherical and conical heads have no simple closed form. This calculator integrates the slices numerically for every head type, and matches the formula above to better than 0.002%.

Partial Volume of a Vertical Tank

A vertical tank is simpler: every horizontal slice is a full circle. With \(a\) the head depth, the liquid fills three zones in order:

Bottom head, \(0 \le h \le a\): volume rises slowly at first, because the head is narrow at the bottom.
Shell, \(a \le h \le a + L\): volume rises in a straight line, \(\pi D^2/4\) per unit of height.
Top head, \(a + L \le h \le 2a + L\): volume rises more slowly again as the head narrows.

Any head shape r(z)\[ V(h) = \int_0^{h} \pi\, r(z)^2 \, dz \]

Ellipsoidal bottom head, h ≤ a\[ V(h) = \frac{\pi R^2 h^2}{a^2}\left(a - \frac{h}{3}\right) \]

Conical bottom, h ≤ a\[ V(h) = \frac{\pi}{3}\left(\frac{R\,h}{a}\right)^2 h \]

Heads hold less than they look. A 2:1 ellipsoidal head holds π D³/24, the same as a piece of shell only D/6 long. On a tall vertical tank, most of the volume is in the straight shell.

Worked Example: Horizontal Tank

A horizontal tank with 2:1 ellipsoidal heads, 96 in inside diameter and 240 in tangent to tangent, filled to 60 in. This is the calculator's Load Example.

R = 48 in, head depth a = 96/4 = 24 in, and R − h = −12 in (more than half full).
\( A = 48^2\cos^{-1}(-0.25) + 12\sqrt{2(48)(60) - 60^2} \) = 4,759.0 in²
Shell: 240 × 4,759.0 = 1,142,160 in³ = 4,944.4 gal.
\( V_{head} = \dfrac{\pi (24)(60^2)(144 - 60)}{6(48)} \) = 79,168 in³ = 342.7 gal per head.
Liquid = 4,944.4 + 2 × 342.7 = 5,629.9 US gal.

Quantity	Value
Shell volume	7,520.2 gal
Each head	501.3 gal
Total volume	8,522.9 gal
Liquid at 60 in	5,629.9 gal
Percent full	66.1%

1 US gal = 231 in³. The level is 62.5% of the diameter but the tank is 66.1% full.

Strapping Tables (Tank Calibration Charts)

Operators measure a tank's contents by level, using a dip stick, a gauge or a level transmitter. A strapping table turns that level into volume. The name comes from "strapping" a tank: measuring its circumference with a steel tape to find the real diameter.

The Strapping Table tab above builds one for any vessel. Set the level increment, then download it as CSV for a spreadsheet, a PLC lookup table or a printed gauge chart.

For custody transfer, measure the real tank. Calculated tables assume a perfect shape. Real tanks are out of round, settle, bulge under load and expand with temperature. Sales and tax measurements use tables from physical calibration, such as API MPMS Chapter 2.

Level transmitters: enter the transmitter's zero point as the level reference. If it sits above the vessel bottom, add that offset before looking up the volume.

Volume Unit Conversions

Unit	US gal	Liters	ft³	m³
1 US gallon	1	3.78541	0.133681	0.00378541
1 imperial gallon	1.20095	4.54609	0.160544	0.00454609
1 oil barrel (bbl)	42	158.987	5.61458	0.158987
1 ft³	7.48052	28.3168	1	0.0283168
1 m³	264.172	1,000	35.3147	1
1,000 in³	4.32900	16.3871	0.578704	0.0163871

Common Mistakes

Outside diameter instead of inside. Volume goes with D², so a 1/4 in wall on a 96 in tank overstates the volume by about 1%.
Overall length instead of tangent to tangent. Using the overall length as L counts the heads twice. For a 2:1 head, this adds half a diameter of shell.
Reading level as percent full. Only a vertical flat-bottom tank is linear. A horizontal tank at 10% of its diameter is only about 5% full.
The wrong level reference. In a vertical vessel, h starts at the bottom of the bottom head, not at the lower tangent line or a nozzle.
Forgetting dead volume. Liquid below the outlet nozzle cannot be pumped out. Subtract it to get usable volume.
Ignoring temperature. Liquids expand. Jet fuel grows about 1% for every 20 °F (11 °C). Correct volumes to a standard temperature for inventory.

Frequently Asked Questions

How do I calculate the volume of a horizontal tank?: Add the shell, π D² L / 4, to the volume of both heads. For a partly full tank, multiply the circular-segment area at the liquid level by L and add the liquid in each head. The calculator above does both for every head type.
How do I find the liquid level for a given volume?: Choose "Volume → level" or "% full → level". There is no closed-form inverse, so the calculator searches for the level that gives that volume.
What is the volume of a 2:1 ellipsoidal head?: π D³ / 24, or about 0.1309 D³. It is half of an ellipsoid of revolution with depth D/4.
What is the volume of an ASME F&D head?: About 0.0810 D³, with a depth of about 0.169 D, for crown radius D and knuckle radius 0.06 D.
Does it work for spheres or capsules?: Yes. Set L = 0 with hemispherical heads for a sphere. Use hemispherical heads with any L for a capsule-shaped tank.
Can I use it for a vertical tank with a cone bottom and a flat roof?: Both ends use the same head here. For a cone-bottom tank, choose Conical and keep the level below the top tangent line; the top head does not affect the volume below it.
Is the wetted area useful?: Yes. Fire-case relief sizing (API 521) and heat-loss calculations use the wetted surface. API 521 limits the fire-exposed wetted area to 25 ft (7.6 m) above grade, which you need to apply separately.

Tank & Vessel Volume Calculator