Tank volume calculator and strapping chart: horizontal and vertical tanks with 2:1, torispherical, hemispherical or flat heads

Every fuel, water or process tank ends up needing two sums: how much it holds, and how much is in it at the height the dipstick reads. In a vertical tank the second is nearly a rule of three; in a horizontal one it is not: the wetted shell is a circular segment, and the heads fill differently. This page does both for the standard heads, with the strapping chart from bottom to top at the step you choose.

The dished head calculator gives each head's depth, blank and weight, and the dished head in petals draws a large head in plate.

Tank volume and strapping chart calculator

Pick the tank position and the heads, and enter the inside diameter, the shell length between the head tangent lines and the table step. Out come the total volume, the volume in the heads, and the chart of level against volume.

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The formulas

The horizontal shell, up to level h

V = L × [a² acos((a − h)/a) − (a − h) √(2ah − h²)] a is the inside radius and L the shell length. The bracket is the circular segment below the level; at half height it is half the circle.

Both 2:1 heads, horizontal

V = (b/a) × π h² (3a − h) / 3 b = a/2 is the depth of a 2:1 head. Together the two heads make an ellipsoid, and the sum is the spherical cap's, shrunk along the axis. Full, π a² b × 4/3.

The vertical tank

V = bottom head up to h + π a² × (h − p) + top head p is the head depth. In the shell the volume grows linearly with the level; in the heads, by the sum of π ρ² slices.

Torispherical heads have no closed form lying horizontal: the calculator adds up slices along each head's axis, each one the circular segment at its own radius, with 200 slices per head.

Worked example

A horizontal tank 96 in inside diameter with 240 in of shell and 2:1 heads holds 8,522.9 US gallons. In metric, 2000 mm by 5000 mm:

1. Full shell: π × 1000² × 5000 = 15.708 m³.
2. Both heads: π × 1000² × 500 × 4/3 = 2.094 m³. Total: 17.802 m³, 17,802 litres.
3. At a 500 mm level: shell 3,070.9 L, heads 327.2 L, total 3,398.2 L, 19.1% of the tank.

Shop notes

1. The dimensions are inside ones. Taking the outside diameter, a 2000 mm tank in 8 mm plate comes out 1.6% bigger on paper.
2. The shell length runs between the tangent lines, where the head's straight flange meets the shell: the straight flange counts as shell.
3. A horizontal tank on a slope: the chart is for a level tank. Tilted, a dipstick in the middle of the tank still reads the total volume only near half height.
4. This chart is geometric. An official calibration chart for a fuel tank comes from measuring the finished tank; this one is for design and for checking.

Frequently asked questions

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

Add the shell and the heads. The full shell is π × radius² × length; up to a level h, it is the circular segment below the level times the length. A 2000 by 5000 mm tank with 2:1 heads holds 17,802 litres.

How do you make a strapping chart for a horizontal tank?

Work out the volume at each dipstick height, from bottom to top. The calculator builds the chart at the step you choose, with the percentage of the tank: in the example, a 500 mm reading is 3,398 litres, 19.1%.

What volume does a 2:1 head hold?

Two thirds of π × radius² × depth, with the depth a quarter of the diameter: π D³ / 24. A 2:1 head of 2000 mm inside diameter holds 1,047 litres.