Horizontal tank (bullet tank) volume calculator

Calculating the volume of an inclined tank with hemispherical heads (caps) is a complex problem because the liquid level is not uniform. This tool uses a numerical integration method to digitally "slice" the tank into thousands of small sections and sum their individual volumes. This allows for high accuracy even when the tank has an angle of inclination. However, it is not based on standards such as ISO 12917-1, as it does not account for deductions due to welds, deformations, pressure changes, or temperature variations. The volume obtained is the actual volume, not corrected to reference conditions.

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Why is it important to know the volume?
Knowing the exact volume of a tank is not just a matter of measurement; it is a fundamental pillar for operational management, safety, and profitability. Accurate calculation is vital for several key reasons:

Inventory and Logistics Management: It allows for precise stock control. Knowing how much product (fuel, raw materials, finished goods) remains in the tank is essential for planning purchases, production, and distribution logistics.

Safety and Regulatory Compliance: Avoiding overfilling is critical. An inaccurate calculation can lead to spills, resulting in safety risks, costly environmental damage, and potential legal penalties. Knowing the available volume prevents these accidents.

Custody Transfer and Trade: When the tank's contents are bought or sold (such as at fuel terminals or in the food industry), the exact volume is the basis of the commercial transaction. Accurate calculation ensures fair trade and is often a requirement for tax certification.

The calculation is based on the disk method, an integral calculus technique. Instead of using a single geometric formula, the script treats the tank as the sum of thousands of small disks or "slices."

 

Decomposition: First, the tank is digitally divided into its three main components: the lower head (lid), the cylindrical body, and the upper head (lid).

1. Slicing: Each of these three sections is divided into thousands of very thin vertical slices (specifically for this calculation, we use 2000 slices per section).

2. Calculation per Slice: For each individual slice, the calculator performs the following:

3. It determines the exact radius of that slice (in the heads, this radius changes; in the cylinder, it is constant).

4. It calculates the precise height of the liquid within that specific slice, compensating for the tank's tilt angle (θ).

5. Using a function, it calculates the exact area that the liquid occupies in that slice.

6. Total Sum: Finally, the area of ​​each slice is multiplied by its thickness to obtain its volume. The sum of the volumes of these thousands of slices (from the three sections) results in the precise total volume shown.

 

If you need to convert that volume to other units, you can go to our volume unit converter by clicking here.

 

Formulas for a horizontal tank with no inclination

With the tank level, the volume at a liquid height h is the sum of the cylindrical shell and the two heads (R = Dᵢ/2):

• Cylinder: Vcyl = L · [R² · acos((R − h)/R) − (R − h) · √(2Rh − h²)]

• Two hemispherical heads (together they form a sphere): Vheads = π · h² · (3R − h) / 3

If the heads are ellipsoidal, with a depth Wₑ smaller than R, the head volume is multiplied by Wₑ/R. When the tank is inclined there is no simple formula any more, which is why the calculator adds up thousands of slices.

 

Worked example

Tank with Dᵢ = 2.00 m (R = 1.00 m), cylinder L = 6.00 m, hemispherical heads (Wₑ = 1.00 m), no inclination and h = 0.80 m:

• Vcyl = 6 × [1² × acos(0.2) − 0.2 × √(1.6 − 0.64)] = 6 × (1.3694 − 0.1960) = 7.041 m³

• Vheads = π × 0.8² × (3 − 0.8) / 3 = 1.474 m³

Volume = 7.041 + 1.474 = 8.515 m³ = 8,515 L (the same result the calculator gives with these inputs).

The total capacity of this tank is 23,038 L. Note that at 40 % of the height (0.80 of 2.00 m) it holds only 37 % of its volume, because the tank is narrower at the bottom. That is why you cannot use a simple proportion with the level.

 

Example table (Dᵢ = 2 m, L = 6 m, hemispherical heads, no inclination)

Height h → volume → % of capacity

0.25 m → 1,540 L → 6.7 %

0.50 m → 4,340 L → 18.8 %

0.80 m → 8,515 L → 37.0 %

1.00 m → 11,519 L → 50.0 %

1.50 m → 18,699 L → 81.2 %

1.75 m → 21,498 L → 93.3 %

2.00 m → 23,038 L → 100 %

 

Frequently asked questions

Which length do I enter: the total or the cylinder?

Only the cylindrical part (L). The depth of each head is entered separately as Wₑ; for hemispherical heads, Wₑ = Dᵢ/2.

What are the angle and the probe distance for?

If the tank is inclined, the level is not the same along the tank. The calculator uses the angle and the position where you measure (the probe) to know the liquid height in each slice.

Does it work for torispherical heads (ASME F&D)?

It treats them as ellipsoids with the depth Wₑ you enter, so for torispherical heads the result is a good approximation, not an exact value.

Does this calculation replace a tank calibration?

No. It is a geometric calculation with nominal dimensions: it does not correct for deformations, weld seams, plate thickness, temperature or pressure. A calibration table (strapping table) with metrological validity requires calibrating the tank. If you need it, we offer ema-accredited tank calibration.