Vertical Oval Tank Volume Calculator

This calculator works out the volume of a vertical oval tank (also called an elliptical tank standing on its end) in litres, US gallons, and cubic metres. You enter the tank’s width, height, and length (the depth from front to back), plus the liquid depth if it is not full, and you get the total and filled volume instantly.

Formula

The volume of a vertical oval tank is found by treating the horizontal cross-section as an ellipse and multiplying by the height (or liquid depth). The formula is:

V = π × (W/2) × (L/2) × H

• V = volume (cubic metres, then converted to litres or gallons)
• W = width of the oval (the longer horizontal axis) in metres
• L = length (the shorter horizontal axis, front-to-back) in metres
• H = height of the tank (or liquid depth) in metres

Because the cross-section is an ellipse, the area is π times the semi-major axis (W/2) times the semi-minor axis (L/2). Multiplying by the vertical dimension gives the volume. To convert cubic metres to litres, multiply by 1000; to US gallons, multiply by 264.172.

Worked Example

Using the default values from the calculator: W = 1.2 m, L = 0.8 m, H = 1.8 m, liquid depth = 1.2 m.

1. Calculate the elliptical area: π × (1.2/2) × (0.8/2) = π × 0.6 × 0.4 = 0.75398 m²
2. Total volume: 0.75398 × 1.8 = 1.35717 m³
3. Convert to litres: 1.35717 × 1000 = 1357.2 L
4. Filled volume: 0.75398 × 1.2 = 0.90478 m³ = 904.8 L
5. US gallons: 1.35717 × 264.172 = 358.5 gal

The calculator shows the same results: total volume 1357.2 L, filled volume 904.8 L, and 358.5 US gallons.

When to Use This Calculator

Vertical oval tanks are common in water storage, chemical dosing, fuel storage, and aquaculture. They are often chosen when floor space is limited but headroom is available. Use this calculator when you need to:

• Determine tank capacity for a new installation
• Estimate how much liquid remains in a partially filled tank
• Check if a tank meets a regulatory or design requirement
• Calculate the volume of a custom-built elliptical tank

The same formula applies whether the tank is made of steel, plastic, or concrete, as long as the interior dimensions are used. Always measure the inside of the tank, not the outside, to avoid errors from wall thickness.

How to Measure a Vertical Oval Tank

Accurate measurements are essential for a correct volume. Follow these steps:

1. Measure the width (W) at the widest point of the oval, from inside wall to inside wall.
2. Measure the length (L) at the deepest point from front to back, again inside.
3. Measure the height (H) from the bottom to the top of the tank, inside.
4. If the tank is not full, measure the liquid depth from the bottom to the liquid surface.

Use the same unit for all measurements. If you measure in feet, convert to metres (1 ft = 0.3048 m) or use a consistent unit and adjust the conversion factor accordingly. The calculator assumes metres, but you can enter any unit as long as you convert the result.

Common Mistakes and How to Avoid Them

• Using outside dimensions – wall thickness can add several percent to the volume. Always measure inside.
• Mixing units – if you measure width in inches and height in feet, the result will be wrong. Convert everything to one unit first.
• Confusing the axes – the width is the longer horizontal dimension; the length is the shorter. Swapping them gives the same area, so it doesn’t affect volume, but it can confuse when you compare with a tank’s nameplate.
• Forgetting the elliptical shape – a vertical oval tank is not a rectangular box. The formula uses π/4 × W × L for the area, not W × L.
• Rounding too early – keep full precision until the final step to avoid cumulative errors.

Limitations of the Formula

The formula assumes a perfect elliptical cross-section and vertical sides. Real tanks may have dished or conical bottoms, rounded corners, or internal baffles that reduce usable volume. In those cases, the calculated volume is an approximation. For tanks with a sloped bottom, the filled volume calculation becomes more complex – you would need to integrate the area up to the liquid level, which is beyond this simple formula.

Also, the formula gives the geometric volume. Actual capacity may be slightly less due to internal fittings, and you should never fill a tank to the absolute brim – leave expansion space for liquids that expand with temperature.

Frequently Asked Questions

How do I convert the result to imperial gallons?

One imperial gallon is 4.54609 litres, so divide the litres by 4.54609. The calculator gives US gallons (3.78541 litres each). For imperial gallons, multiply the US gallon result by 0.83267.

What if my tank has a dished bottom?

A dished or rounded bottom adds volume that the simple elliptical formula does not capture. For a rough estimate, you can treat the bottom as a partial sphere or ellipsoid and add that volume. For exact numbers, consult the tank manufacturer’s calibration chart.

Can I use this for a horizontal oval tank?

No. A horizontal oval tank has a different geometry – the cross-section is an ellipse, but the liquid surface is not horizontal across the full width. The volume of a partially filled horizontal tank requires a more complex formula involving the segment of an ellipse. This calculator is only for vertical tanks where the liquid surface is always parallel to the elliptical base.

Why does the calculator show litres and US gallons but not cubic feet?

The calculator focuses on the most common units for tank volume. To get cubic feet, divide the volume in cubic metres by 0.0283168. For example, 1.357 m³ is about 47.9 cubic feet.

How accurate is the volume if I measure in inches?

If you convert inches to metres correctly (1 inch = 0.0254 m), the result is just as accurate. The key is to convert all three dimensions consistently. Many users find it easier to measure in centimetres and divide by 100 to get metres.

Does the wall thickness matter?

Yes, but only if you use outside dimensions. The volume is based on interior dimensions. For a steel tank with 6 mm walls, the difference can be about 1–2% of the volume, which matters for precise chemical dosing but is negligible for general water storage.

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in w | Width | m | 1.2 | 0
in h | Height | m | 1.8 | 0
in l | Length (depth) | m | 0.8 | 0
in fl | Liquid depth | m | 1.2 | 0
out vol | Total volume | L | (pi * w/2 * l/2 * h) * 1000 | 1
out fvol | Filled volume | L | (pi * w/2 * l/2 * fl) * 1000 | 1
out usg | Total volume (US gal) | gal | (pi * w/2 * l/2 * h) * 264.172 | 1