Horizontal Cylinder Tank Volume Calculator & Formula

This calculator works out the volume of liquid currently held in a horizontal cylindrical tank, plus the total tank capacity and the percentage filled. You enter the tank diameter, total length, and the depth of the liquid, and you get the filled volume in your choice of units, along with the remaining capacity. The calculation uses the standard segment-area formula for a partially filled horizontal cylinder, which is the same method used in industrial tank gauging.

Formula

The liquid volume in a horizontal cylindrical tank is found by multiplying the cross‑sectional area of the liquid segment by the tank length. The segment area is derived from the circular segment formula:

V = L × [ r² × acos((r − h)/r) − (r − h) × √(2rh − h²) ]

• V = liquid volume (m³, ft³, litres, gallons, etc.)
• L = total length of the cylindrical shell (m, ft)
• r = inside radius of the tank = diameter/2 (m, ft)
• h = depth of liquid measured from the lowest point of the tank bottom to the liquid surface (m, ft)
• acos = inverse cosine, in radians

The total capacity is simply the volume of a full cylinder: V_full = π × r² × L. The fill percentage is the liquid volume divided by the total capacity, multiplied by 100.

Worked Example

Using the default values from the calculator above: diameter = 2 m, length = 4 m, liquid depth = 0.8 m.

1. Radius: r = 2 / 2 = 1 m
2. Compute the term (r − h): 1 − 0.8 = 0.2 m
3. Compute 2rh − h²: 2×1×0.8 − 0.8² = 1.6 − 0.64 = 0.96 m²
4. Square root: √0.96 ≈ 0.9799 m
5. Compute acos((r − h)/r) = acos(0.2/1) = acos(0.2) ≈ 1.3694 radians
6. Segment area = 1² × 1.3694 − 0.2 × 0.9799 = 1.3694 − 0.1960 = 1.1734 m²
7. Liquid volume = 4 × 1.1734 = 4.6936 m³ → rounded to 4.694 m³

The calculator shows 4.694 m³ for the liquid volume, matching this step‑by‑step result. Total capacity = π × 1² × 4 = 12.566 m³, and fill percentage = (1.1734 / 3.1416) × 100 ≈ 37.3%.

Why the Formula Works

A horizontal cylinder is essentially a prism whose cross‑section is a circle. When the cylinder is not full, the liquid occupies a circular segment – the region between a chord (the liquid surface) and the arc of the circle below it. The formula for the area of a circular segment is a standard geometric result: it subtracts the triangular area (r − h)√(2rh − h²) from the sector area r²·acos((r−h)/r). Multiplying that area by the tank length gives the volume. This assumes the tank ends are flat and the cylinder is perfectly horizontal; dished or elliptical heads add a small extra volume that this simple model ignores (see “Limitations” below).

How to Use the Calculator Correctly

• Measure the inside diameter – not the outside – because wall thickness reduces the usable volume. If you only have the outside diameter, subtract twice the wall thickness.
• Measure the liquid depth from the lowest point of the inside bottom of the tank, not from the ground or from a dipstick reading that starts at a different zero point.
• Keep all units consistent. If you measure diameter in feet, length in feet, and depth in feet, the volume comes out in cubic feet. Convert to gallons or litres using standard factors (1 ft³ = 7.48052 US gallons, 1 m³ = 1000 litres).
• For a tank lying on its side, the length is the horizontal dimension along the cylinder axis, not the height.
• Check the fill percentage. If the result is above 100% or below 0%, you likely entered a liquid depth larger than the diameter or a negative value.

Common Mistakes and Misconceptions

• Using the diameter instead of the radius. The formula requires r. A common error is plugging in the diameter directly, which overestimates the volume by a factor of 4.
• Forgetting to convert units. Mixing metres and centimetres (or feet and inches) without conversion yields wildly wrong volumes.
• Assuming the tank is a vertical cylinder. A vertical cylinder uses a simple πr²h formula; the horizontal case is more complex because the cross‑section changes with depth.
• Ignoring the end caps. Many tanks have dished (torispherical or elliptical) heads that add 5–10% to the total capacity. For precise inventory, you need a formula that accounts for the head shape.
• Measuring liquid depth from the top. Some dipsticks read from the top down. If you have the ullage (space above the liquid), subtract it from the diameter to get the actual depth.

Limitations of the Simple Cylinder Formula

The formula above assumes a perfectly horizontal, perfectly cylindrical tank with flat ends. Real tanks often have:

• Dished heads (elliptical, torispherical, or hemispherical) – these add volume that varies non‑linearly with fill level. For a rough estimate, you can add the head volume as a fixed percentage, but for accurate gauging you need a more detailed calculation.
• Slight slope – if the tank is installed with a small incline for drainage, the liquid surface is not parallel to the ends, and the volume differs slightly from the horizontal case.
• Internal fittings – baffles, heating coils, or agitators displace liquid and reduce the true volume.
• Thermal expansion – liquids expand with temperature, so the volume at a given depth changes with temperature. The calculator gives the geometric volume, not the mass.

For most practical purposes – estimating fuel in a storage tank, water in a septic tank, or chemical in a process vessel – the simple formula is accurate to within a few percent, which is acceptable for non‑critical use.

Practical Applications and Alternatives

This calculator is useful for:

• Estimating how much liquid remains in a horizontal storage tank (fuel, water, chemicals) without a level sensor.
• Checking the calibration of a dipstick or sight glass.
• Planning deliveries or transfers when you know the tank dimensions and current depth.
• Designing a new tank – you can vary diameter and length to see the capacity and fill behaviour.

If your tank is not horizontal, use a vertical cylinder calculator (V = πr²h). If it has dished heads, look for a tank volume calculator that includes head volume, or use a strapping table from the manufacturer. For irregular shapes, the only reliable method is a calibration chart produced by measuring actual volumes.

Frequently Asked Questions

What if my tank is not exactly horizontal?

If the tank is tilted, the liquid surface is not perpendicular to the cylinder axis, and the volume is slightly different. For small slopes (less than 1°), the error is negligible. For larger slopes, you need a more complex integration or a calibration table.

How do I convert cubic metres to litres or gallons?

1 cubic metre = 1000 litres. 1 cubic foot = 7.48052 US gallons (or 6.22884 imperial gallons). Multiply the volume in cubic metres by 1000 to get litres, or multiply cubic feet by 7.48052 to get US gallons.

Can I use this for a tank with elliptical heads?

Not directly. The formula only covers the cylindrical shell. Elliptical heads add volume that depends on the head shape and fill level. For a rough estimate, you can add 5–10% of the shell volume, but for accurate measurement, use a tank strapping table or a calculator that includes head volume.

Why does the volume not increase linearly with depth?

Because the cross‑sectional area of a circle is not linear with depth. Near the bottom, a small increase in depth adds a small area; near the middle, the same depth increase adds a much larger area. This is why the fill percentage curve is S‑shaped.

What is the maximum liquid depth I can enter?

The depth cannot exceed the diameter. If you enter a depth greater than the diameter, the formula will produce an invalid result (the square root term becomes negative). The calculator’s minimum is set to 0, but it does not enforce a maximum – you must ensure h ≤ d.

Does the calculator account for the thickness of the tank walls?

No. It uses the dimensions you enter. For accurate results, enter the inside diameter and inside length. If you only know outside dimensions, subtract twice the wall thickness from the outside diameter and subtract twice the wall thickness from the length (if the ends are flat).

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in d | Tank diameter | m | 2 | 0
in L | Tank length | m | 4 | 0
in h | Liquid depth | m | 0.8 | 0
out vol | Liquid volume | m³ | L * ( (d/2)^2 * acos(1 - 2*h/d) - (d/2 - h) * sqrt(2*h*d - h^2) ) | 3
out cap | Total capacity | m³ | pi * (d/2)^2 * L | 3
out pct | Fill percentage | % | ( (d/2)^2 * acos(1 - 2*h/d) - (d/2 - h) * sqrt(2*h*d - h^2) ) / (pi * (d/2)^2) * 100 | 1