Hexagon Aquarium Volume Calculator

This calculator works out the water volume of a hexagon-shaped aquarium in US gallons and litres. You enter the length of one side, the height of the tank, and the distance from the centre to one side (the apothem), and it returns the total volume, accounting for the hexagonal footprint.

Formula

For a regular hexagon (all six sides equal), the volume is the area of the hexagonal base multiplied by the height of the tank. The area of a regular hexagon is given by:

Area = (3√3 / 2) × s²

where s is the length of one side. Then multiply by the height h to get the volume in cubic inches. To convert to US gallons, divide by 231 (since 1 US gallon = 231 cubic inches). To convert to litres, multiply the cubic inches by 0.0163871.

If you prefer using the apothem (the distance from the centre to the midpoint of a side), the area is simply Area = (1/2) × perimeter × apothem. For a regular hexagon, perimeter = 6 × s, so Area = 3 × s × apothem. Both methods give the same result for a true regular hexagon.

Worked Example

Using the default values from the calculator: side length = 12 in, height = 18 in, apothem = 10.4 in (which is approximately 12 × √3/2).

1. Calculate the base area using the side formula: (3√3 / 2) × 12² = (3 × 1.732 / 2) × 144 = 2.598 × 144 = 374.112 in².
2. Multiply by height: 374.112 × 18 = 6734.016 in³.
3. Convert to US gallons: 6734.016 / 231 = 29.15 gallons.
4. Convert to litres: 6734.016 × 0.0163871 = 110.35 litres.

The calculator shows 29.15 US gallons and 110.4 litres, matching the example.

Why Use a Hexagon Tank?

Hexagon aquariums are popular for their aesthetic appeal and the unique viewing angles they offer. They can fit into corners or serve as striking centrepieces. However, their volume is not as straightforward to calculate as a standard rectangular tank, which is why a dedicated calculator is handy. Knowing the exact volume is crucial for dosing medications, determining heater wattage, and stocking fish appropriately.

How to Measure Your Hexagon Tank

To get accurate results, measure the following in inches (or centimetres, but the calculator here uses inches):

• Side length: Measure one of the six equal sides from edge to edge, not including the glass thickness.
• Height: Measure from the bottom inside to the top inside edge, again not including glass thickness.
• Apothem: If you don’t have this, you can calculate it as side × √3/2 for a regular hexagon. For a side of 12 in, that’s 12 × 0.866 = 10.392 in. The default 10.4 is close enough.

If your tank is not a perfect regular hexagon (some are elongated or irregular), the formula will be approximate. In that case, measure the apothem directly from the centre of the tank to the midpoint of one side.

Common Mistakes and Misconceptions

One frequent error is using the distance across the tank (from one vertex to the opposite vertex) instead of the side length. The formula requires the side length, not the diameter. Another mistake is forgetting to subtract glass thickness when measuring from the outside. Always measure inside dimensions for water volume. Also, note that the volume you calculate is the total capacity; the actual water volume will be slightly less because of substrate, decorations, and the fact that you don’t fill to the brim. A good rule of thumb is to fill to about 1 inch below the top.

How to Read the Result

The calculator gives two outputs: US gallons and litres. For fish stocking, the general guideline is 1 inch of fish per gallon, but this is a rough estimate and depends on the species and filtration. For medication dosing, always follow the instructions on the product, and use the actual water volume (after subtracting displacement from substrate and decor) rather than the bare tank volume. For heater sizing, a common recommendation is 3 to 5 watts per gallon, but this varies with ambient temperature and tank location.

Limitations of the Formula

The formula assumes a perfect regular hexagon with vertical sides. Many commercial hexagon tanks are actually truncated pyramids—the bottom is smaller than the top. In that case, the volume is less than a straight-sided calculation. If your tank tapers, measure the bottom side length and the top side length, then use the average for a closer estimate. Alternatively, you can treat it as a prism with a trapezoidal cross-section, but that requires more complex math. For most practical purposes, the regular hexagon formula gives a good approximation, but be aware of the potential overestimation.

Frequently Asked Questions

How do I find the apothem if I only know the side length?

For a regular hexagon, the apothem equals the side length multiplied by √3/2. For example, a side of 10 inches gives an apothem of 10 × 0.866 = 8.66 inches. You can enter that in the calculator, but the side-length formula already uses it implicitly.

Does the calculator account for the glass thickness?

No, you must measure the inside dimensions. If you measure the outside, subtract twice the glass thickness from the side length and height. For a typical 1/4-inch glass, subtract 0.5 inches from each dimension.

Can I use this for a hexagonal bowl or a non-aquarium container?

Yes, as long as the container is a regular hexagon prism (straight sides), the formula applies. For a bowl with curved sides, it’s not accurate. For any container, just measure the inside dimensions.

What is the difference between US gallons and imperial gallons?

US gallons are smaller: 1 US gallon = 3.78541 litres, while 1 imperial gallon = 4.54609 litres. This calculator uses US gallons. If you need imperial, multiply the US gallons by 0.83267.

Why does my tank’s actual water volume seem less than the calculated volume?

Because you don’t fill to the very top, and substrate, rocks, and decorations displace water. A typical 29-gallon hexagon might hold about 24-26 gallons of actual water once set up. Always account for displacement when dosing chemicals or stocking fish.

Is a hexagon tank more expensive to heat than a rectangle?

Not necessarily. The surface area to volume ratio is what matters. Hexagons have a slightly higher surface area per unit volume than cubes, so they may lose heat a bit faster, but the difference is small. Choose a heater based on the actual water volume and the temperature difference you need.

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in side | Side length | in | 12 | 0
in h | Height | in | 18 | 0
in ap | Apothem (centre to side) | in | 10.4 | 0
out gal | Volume (US gallons) | US gal | (3 * sqrt(3) / 2 * side^2 * h) / 231 | 2
out lit | Volume (litres) | L | (3 * sqrt(3) / 2 * side^2 * h) * 0.0163871 | 1