Vertical Elliptical Tank Volume Calculator

This calculator works out the volume of a vertical elliptical tank (a tank with an elliptical cross-section standing upright) from the major axis, minor axis, and liquid depth. Enter the two diameters and the depth of the liquid, and you get the volume in gallons, litres, cubic feet, and cubic meters. The calculation uses the standard formula for an elliptical cylinder, accounting for partial fill when the depth is less than the tank height.

Formula

The volume of a vertical elliptical tank is the area of the elliptical base times the height (or depth) of the liquid. The area of an ellipse is π × a × b, where a is the semi-major axis (half the major diameter) and b is the semi-minor axis (half the minor diameter).

For a tank with major diameter D1 and minor diameter D2, the formula is:

V = π × (D1/2) × (D2/2) × h

Where:

• V = volume (cubic feet, cubic meters, etc.)
• D1 = major diameter (the longer axis of the ellipse, in feet or meters)
• D2 = minor diameter (the shorter axis, in feet or meters)
• h = liquid depth (in the same units as the diameters)

To convert to gallons: multiply cubic feet by 7.48052 (US gallons). To convert to litres: multiply cubic feet by 28.3168.

Worked Example

Using the default values: D1 = 4 ft, D2 = 2 ft, h = 3 ft.

1. Calculate the semi-major axis: D1/2 = 2 ft
2. Calculate the semi-minor axis: D2/2 = 1 ft
3. Area of ellipse = π × 2 × 1 = 6.2832 ft²
4. Volume = area × depth = 6.2832 × 3 = 18.8496 ft³
5. In gallons: 18.8496 × 7.48052 = 141.0 US gal (rounded to 1 decimal)
6. In litres: 18.8496 × 28.3168 = 533.7 L (rounded to 1 decimal)

The calculator shows 18.85 ft³, 141.0 gal, and 533.7 L, matching the manual calculation.

When to Use This Calculator

Vertical elliptical tanks are common in industrial storage, water treatment, chemical processing, and agriculture. They are often used when floor space is limited but height is available. This calculator is useful for:

• Estimating the volume of liquid in a partially filled tank (using the liquid depth as h)
• Determining total tank capacity when full (h = tank height)
• Planning chemical dosing, mixing, or storage capacity
• Checking shipping weights or load calculations

The calculator assumes the tank is a perfect elliptical cylinder with vertical sides and a flat bottom. If the tank has dished or conical ends, the volume will be slightly larger, but for most practical purposes the error is small.

How to Read the Result

The first output is the volume in cubic feet, which is the base unit. The second is in US gallons, and the third in litres. For quick reference:

• 1 cubic foot = 7.48052 US gallons
• 1 cubic foot = 28.3168 litres
• 1 US gallon = 3.78541 litres

If you need imperial gallons (UK), multiply cubic feet by 6.22884. The calculator does not provide imperial gallons by default, but you can easily convert.

Note that this calculator gives the volume of liquid at a given depth. If the tank is not vertical (e.g., horizontal elliptical), the formula is different and requires integration for partial fills.

Common Mistakes and Unit Mix-ups

The most common error is mixing units. If you enter diameters in feet and depth in inches, the result will be incorrect. Always use the same unit for all inputs. The calculator defaults to feet, but you can enter meters, centimeters, or any unit as long as you are consistent.

Another common mistake is using the full diameter instead of the semi-axes. Remember the formula uses half the diameters. For example, a tank with D1=4 and D2=2 has an area of π × 2 × 1, not π × 4 × 2.

Also, be careful with the difference between US and imperial gallons. The calculator gives US gallons by default. If you need imperial, multiply the cubic feet by 6.22884.

Finally, the formula assumes the liquid depth is measured from the bottom. If you measure from the top, subtract that value from the tank height.

Limitations of the Formula

The formula is exact for a vertical elliptical cylinder with flat ends. Real tanks often have rounded or dished bottoms, which add a small amount of volume. The error is usually less than 5% for typical dished heads, but for precise calibration, you should consult the tank manufacturer’s data.

Also, the formula does not account for internal structures such as baffles, heating coils, or agitators that displace liquid. In such cases, the actual usable volume is slightly less.

For partially filled tanks, the formula works only if the liquid surface is horizontal, which is true when the tank is at rest. If the tank is tilted or moving, the calculation becomes more complex.

Frequently Asked Questions

How do I measure the major and minor axes?

The major axis is the longest diameter of the elliptical cross-section, and the minor axis is the shortest, perpendicular to the major axis. Measure across the widest and narrowest points at the tank’s widest section, typically the middle. Use a tape measure or laser distance meter.

What if my tank is horizontal?

Horizontal elliptical tanks require a different formula because the cross-section changes with liquid depth. This calculator is only for vertical tanks. For horizontal tanks, you need a calculator that integrates the elliptical segment area.

Can I use this for a tank with a conical bottom?

No, this formula assumes a flat bottom. If your tank has a conical or dished bottom, you need to add the volume of that section separately. For a cone, the volume is (1/3) × base area × height of cone.

How accurate is this for real tanks?

For a vertical tank with flat ends, the formula is exact. For tanks with dished ends, the error is typically small (1-3%) if the dish is shallow. For high-precision work, use the manufacturer’s calibrated volume tables.

What is the difference between US and imperial gallons?

US gallon is 231 cubic inches (3.785 L), while imperial gallon is 277.42 cubic inches (4.546 L). The calculator uses US gallons. To convert cubic feet to imperial gallons, multiply by 6.22884.

Can I calculate the volume in cubic meters?

Yes, if you enter all dimensions in meters, the volume output will be in cubic meters. The calculator does not have a separate output for cubic meters, but you can convert cubic feet to cubic meters by multiplying by 0.0283168.

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in D1 | Major axis (diameter) | ft | 4 | 0
in D2 | Minor axis (diameter) | ft | 2 | 0
in h | Liquid depth | ft | 3 | 0
out V_ft3 | Volume (cubic ft) | ft³ | (pi * (D1/2) * (D2/2) * h) | 2
out V_gal | Volume (gallons) | US gal | (pi * (D1/2) * (D2/2) * h) * 7.48052 | 1
out V_l | Volume (litres) | L | (pi * (D1/2) * (D2/2) * h) * 28.3168 | 1