Horizontal Tank Volume Calculator Equation

This calculator works out the volume of liquid in a horizontal cylindrical tank when you enter the tank diameter, tank length, and liquid depth. It returns the volume in your chosen units (liters, gallons, cubic feet, etc.) and also gives the percentage of the tank that is filled. The calculation uses the standard formula for the area of a circular segment multiplied by the tank length, which accounts for the curved bottom of the tank.

Formula

The volume V of liquid in a horizontal cylindrical tank is the cross‑sectional area of the liquid (a circular segment) times the tank length L:

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

where:

• V = liquid volume (m³, ft³, liters, gallons – same unit as L and r)
• L = length of the cylindrical tank (m or ft)
• r = radius of the tank = diameter / 2 (m or ft)
• h = depth of the liquid measured from the bottom of the tank (m or ft)
• acos is the inverse cosine (angle in radians)
• √ is the square root

All length units must be the same (e.g., all meters or all feet). The result will be in cubic units of that length (m³ or ft³). To get liters, multiply m³ by 1000; to get US gallons, multiply ft³ by 7.48052.

Worked Example

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

1. Radius r = 2 / 2 = 1 m
2. Compute (r − h) = 1 − 0.8 = 0.2 m
3. Compute 2rh − h² = 2×1×0.8 − 0.8² = 1.6 − 0.64 = 0.96
4. √0.96 ≈ 0.9799
5. Compute acos( (r − h)/r ) = acos(0.2/1) = acos(0.2) ≈ 1.3694 radians
6. Area = r² × 1.3694 − 0.2 × 0.9799 = 1.3694 − 0.1960 = 1.1734 m²
7. Volume = 4 × 1.1734 = 4.6936 m³

The calculator shows 4.694 m³, which matches (rounded to three decimals). That is about 4,694 liters or 1,240 US gallons.

When to Use This Formula

This formula applies to a perfectly horizontal cylinder with flat ends (or any ends, as long as the cylindrical section is horizontal). It is commonly used for:

• Fuel storage tanks on farms or industrial sites
• Water tanks on trucks or trailers
• Chemical storage vessels
• Propane and other pressurized gas tanks (when lying horizontally)

The formula works for any liquid depth from 0 (empty) to the full diameter (completely full). When h = d, the segment becomes a full circle and the volume equals πr²L, which is the total cylinder volume.

How to Read the Result

The volume output is the actual liquid content, not the total tank capacity. The fill percentage tells you how full the tank is by depth, not by volume – because the tank is curved, a depth of 50% does not mean 50% of the volume. For example, in a horizontal cylinder, 50% depth gives about 50% volume only if the tank is perfectly half‑full; but a depth of 25% gives much less than 25% volume because the lower part is narrower. The calculator’s percentage is simply h/d × 100, which is a depth percentage. If you need a volume percentage, divide the calculated volume by the total cylinder volume (πr²L) and multiply by 100.

Common Mistakes and Pitfalls

• Unit mix‑ups: Mixing meters and centimeters, or feet and inches, will ruin the result. Convert everything to one unit first.
• Using the wrong diameter: The formula uses the inside diameter of the tank. If you measure the outside diameter, subtract twice the wall thickness.
• Forgetting the radius: The formula uses radius, not diameter. Many people accidentally plug in the diameter as r.
• Depth measured from the top: The liquid depth must be from the bottom of the tank. If you have a dipstick reading from the top (ullage), subtract that from the diameter to get h.
• Rounding too early: The acos and sqrt terms are sensitive; keep several decimal places until the final step.

Limitations and Alternatives

This formula assumes the tank is a perfect cylinder and perfectly horizontal. Real tanks may have dished or elliptical heads, which add extra volume at the ends. For tanks with heads, the formula under‑estimates the true volume, especially when the tank is nearly full. If you need extreme accuracy for a tank with heads, you need a more complex formula that includes the head shape (ellipsoidal, torispherical, etc.). Also, if the tank is slightly tilted, the liquid surface is not a flat horizontal plane relative to the cylinder axis, so the simple segment formula fails. For tilted tanks, numerical integration or a calibration chart is required.

Another practical alternative is to use a dip chart or strapping table, which is a table of liquid depth versus volume, often supplied by the tank manufacturer. Those tables are created by measuring the actual tank and are more accurate than any generic formula for a specific tank.

Frequently Asked Questions

How do I convert the volume to liters or gallons?

If you use meters for length, the volume is in cubic meters. Multiply by 1000 to get liters. If you use feet, the volume is in cubic feet. Multiply by 7.48052 to get US gallons, or by 6.22884 to get imperial gallons.

Does the formula work for a tank lying on its side?

Yes, that is exactly what this formula is for – a horizontal cylinder. The liquid depth is measured from the bottom of the cylinder’s side. If the tank is vertical, the volume is simply πr²h, which is much simpler.

What if the liquid depth is more than the radius?

The formula still works. The acos term will be between 0 and π, and the (r − h) term becomes negative, which is correct because the segment area is more than half the circle. For example, if h = 1.5 m in a 2 m diameter tank, the formula gives about 85% of the full volume.

Why does 50% depth not equal 50% volume?

Because the cross‑section of a horizontal cylinder is a circle, and the area of a circular segment is not linear with depth. At 50% depth, the area is exactly half the circle (since the chord is the diameter), so the volume is exactly 50% – actually that is one case where it does match. But at 25% depth, the area is about 19.5% of the circle, not 25%. The relationship is only linear at 0%, 50%, and 100%.

Can I use this for a tank with elliptical heads?

Not directly. The formula only covers the cylindrical section. For a tank with heads, you add the volume of the heads, which depends on their shape. For a 2:1 ellipsoidal head, the head volume is about π × (d/2)² × (d/4) / 2. Many online calculators include head volume as an option.

How accurate is this formula for a real tank?

For a perfectly cylindrical, horizontal tank with flat ends, it is mathematically exact. For real tanks, accuracy depends on how close the tank is to a perfect cylinder, how precisely you measure the dimensions, and whether the tank is truly level. In practice, expect errors of 1–3% if you measure carefully, and more if the tank is dented or has internal structures.

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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 pct | Fill percentage | % | h / d * 100 | 1