Horizontal Tank Volume Calculator Excel

This calculator works out the volume of a horizontal cylindrical tank (like a fuel storage tank or a propane cylinder lying on its side) from the tank’s diameter, length, and the depth of liquid inside it. You enter the tank dimensions and the liquid depth, and you get back the volume in your choice of units (liters, gallons, cubic meters, etc.) as well as the percentage of the tank’s total capacity that is filled. The calculator uses the standard formula for the area of a partially filled horizontal cylinder segment, which is the same method used in many Excel spreadsheets and engineering references.

Formula

The volume of liquid in a horizontal cylindrical tank is calculated by multiplying the cross-sectional area of the liquid segment by the length of the tank. The cross-sectional area is derived from the geometry of a circle, where the liquid fills a circular segment. The formula is:

V = L × (r² × (θ – sin θ))

Where:

• V = volume of liquid (m³, liters, gallons, etc.)
• L = length of the tank (m, ft, etc.)
• r = radius of the tank = diameter / 2 (m, ft)
• θ = angle of the liquid segment in radians, calculated as θ = 2 × arccos((r – h) / r)
• h = depth of liquid from the bottom of the tank (m, ft)

Alternatively, a common equivalent form uses the fraction of the diameter filled (k = h/d) and the formula:

V = L × (d²/8) × (arccos(1 – 2k) – (1 – 2k) × sqrt(1 – (1 – 2k)²))

This version is convenient because it directly uses the diameter and the liquid depth ratio. The calculator above uses this form, with the arccos function in radians (which matches the standard math functions in Excel and most programming languages).

Worked Example

Using the default values from the calculator: tank diameter (d) = 2 m, length (L) = 4 m, liquid depth (h) = 0.5 m.

1. Calculate the fill ratio: k = h / d = 0.5 / 2 = 0.25
2. Compute the term (1 – 2k) = 1 – 0.5 = 0.5
3. Compute arccos(0.5) in radians = 1.0472 (since cos(60°) = 0.5, and 60° = π/3 ≈ 1.0472 rad)
4. Compute sqrt(1 – 0.5²) = sqrt(1 – 0.25) = sqrt(0.75) ≈ 0.8660
5. Now the bracket: (1.0472 – 0.5 × 0.8660) = (1.0472 – 0.4330) = 0.6142
6. Multiply by (d²/8) = (2²/8) = 4/8 = 0.5, so area = 0.5 × 0.6142 = 0.3071 m²
7. Volume = area × length = 0.3071 × 4 = 1.2284 m³

The calculator rounds to three decimal places, giving 1.228 m³. The fill percentage is simply (h/d) × 100 = 25.0%, and the total tank volume is π × (1)² × 4 = 12.566 m³ (rounded to 12.566).

Why Use a Horizontal Tank Volume Calculator?

Horizontal cylindrical tanks are common in fuel storage, chemical processing, water treatment, and agriculture. Unlike vertical tanks where volume is a simple product of base area and height, horizontal tanks have a non-linear relationship between liquid depth and volume. The same depth increase near the bottom adds less volume than near the middle, because the cross-section widens. This calculator removes the need to look up charts or manually integrate the segment area.

It is especially useful for:

• Estimating how much liquid remains in a tank when you only have a dip stick reading (depth).
• Calibrating tank level sensors or sight glasses.
• Checking delivery quantities against tank capacity.
• Designing containment or overflow systems.

How to Use the Calculator and Read the Results

Enter the tank’s internal diameter and length in consistent units (both in meters, both in feet, etc.). Then enter the liquid depth as measured from the bottom of the tank, in the same unit. The calculator returns the liquid volume in cubic meters (or cubic feet if you used feet) and the fill percentage. To get liters, multiply cubic meters by 1000. To get US gallons, multiply cubic meters by 264.172. To get imperial gallons, multiply by 219.969.

The fill percentage is simply the depth divided by the diameter, expressed as a percent. It is not the same as the volume percentage, which is lower than the depth percentage for depths below 50% and higher for depths above 50%. For example, at 25% depth, the volume is about 19.5% of total (as seen in the example: 1.228/12.566 = 9.77%? Wait, that’s not right – let’s correct that). Actually, in the example, 1.228 m³ is 9.77% of 12.566 m³, not 19.5%. The depth is 25%, but the volume is only about 9.8%. This illustrates the non-linearity. The calculator shows both the depth percentage and the volume percentage (as the ratio of the computed volume to the total volume). In the example, the volume percentage is (1.228/12.566)*100 = 9.8%, which is not shown directly but can be derived.

Common Mistakes and Limitations

• Unit mismatch: Ensure diameter, length, and depth are all in the same unit. Mixing meters and centimeters will give wildly wrong results.
• Using the wrong formula: Some formulas assume the tank is vertical. For horizontal tanks, the segment area formula is required.
• Ignoring tank ends: This calculator assumes flat, vertical ends. If the tank has dished or elliptical heads, the volume will be slightly larger (typically 5-10% for the heads). For precise measurements, add the head volume separately.
• Depth greater than diameter: The formula only works for h between 0 and d. If h > d, the tank is overflowing; cap h at d for full capacity.
• Temperature effects: Liquids expand with temperature. The calculator gives volume at the current temperature; for high-accuracy custody transfer, apply temperature correction factors.

Excel Implementation

Many people want to build this in Excel. The formula in Excel uses the ACOS function (which returns radians) and SQRT. For a tank with diameter in cell A1, length in B1, and depth in C1, the volume in cubic meters is:

=B1*(A1^2/8)*(ACOS(1-2*C1/A1)-(1-2*C1/A1)*SQRT(1-(1-2*C1/A1)^2))

Make sure to use consistent units. If you want liters, multiply by 1000. If you want gallons, multiply by the appropriate conversion factor. This formula is exactly what the calculator uses.

When to Use This vs. Other Tank Shapes

Horizontal cylinders are one of several common tank geometries. Vertical cylinders use a simple cylinder volume (πr²h). Spherical tanks use a different segment formula. Rectangular tanks are trivial (length × width × height). If your tank has dished ends, you need to add the volume of the heads, which depends on the head type (elliptical, torispherical, etc.). For most practical purposes, the horizontal cylinder formula is accurate to within a few percent for tanks with flat ends.

Frequently Asked Questions

Q: How do I convert the volume result to gallons?
A: If you entered dimensions in meters, the volume is in cubic meters. Multiply by 264.172 to get US gallons, or by 219.969 for imperial gallons. If you entered in feet, the volume is in cubic feet; multiply by 7.48052 for US gallons.

Q: What if my tank has rounded ends?
A: The calculator assumes flat ends. For dished heads, add the volume of the heads separately. A common approximation for elliptical heads is to add the volume of a sphere of the same diameter times a factor (e.g., 0.1 to 0.2 for typical heads). For precise values, use head volume formulas or tank calibration charts.

Q: Can I use this for a partially filled tank that is not level?
A: No, this formula assumes the tank is level and the liquid surface is horizontal. If the tank is tilted, the volume calculation becomes more complex and requires integration along the length.

Q: Why is the volume percentage different from the depth percentage?
A: Because the cross-sectional area of a horizontal cylinder is not linear with depth. Near the bottom and top, a small depth change adds little area; near the middle, it adds a lot. So at 25% depth, the volume is only about 10% of total, as seen in the example.

Q: What is the maximum depth I can enter?
A: The depth cannot exceed the diameter. If you enter a depth greater than the diameter, the formula will attempt to take the square root of a negative number, which is invalid. The calculator will show an error. For a full tank, use depth = diameter.

Q: Does this work for any liquid?
A: Yes, the volume calculation is independent of the liquid type. It only depends on the tank geometry and the liquid depth. However, for very viscous liquids that don’t settle level, the measurement may not be accurate.

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in d | Tank diameter | m | 2 | 0
in L | Tank length | m | 4 | 0
in h | Liquid depth | m | 0.5 | 0
out vol | Liquid volume | m³ | (L * (d*d/8 * (acos(1-2*h/d) - (1-2*h/d)*sqrt(1-(1-2*h/d)^2)))) | 3
out pct | Fill percentage | % | (h/d*100) | 1
out total | Total tank volume | m³ | (pi * (d/2)^2 * L) | 3