The formula uses the area of a regular hexagon, which is about 2.6 times the side length squared. A hexagon with 12-inch panels has a floor of 374 square inches, slightly more than a 19-inch square.
How to measure a hexagon tank
- Measure the inside width of one glass panel, from corner seam to corner seam.
- If the panels differ in width, the tank is not regular; the flat back hexagon calculator handles the most common irregular case.
- Do not confuse side length with the width across the tank. Face-to-face width is 1.732 × side; corner-to-corner width is 2 × side.
Always measure inside the glass. Exterior sizes include the panel thickness and any trim, which on larger tanks can remove 5 to 10 percent of the apparent volume. See the measuring guide for the full method.
Hexagon volume formula
V = (3√3 ÷ 2) × s² × H
A regular hexagon has area 2.598 × s². Multiply by height. The side length is the width of one of the six glass panels.
With inches, divide the cubic result by 231 to get US gallons and multiply gallons by 3.785 for litres. With centimetres, divide by 1,000 for litres directly.
Worked example
Inputs: Side Length 12 inHeight 24 in
2.598 × 12² × 24 = 8,979 in³, which is 38.9 US gallons or 147.1 litres.
Side length versus face-to-face width
The easiest tank-wide measurement on a hexagon is between two opposite flat panels. That distance is √3 times the side length, so divide it by 1.732 to get the value this calculator needs. Measuring corner to corner gives twice the side length instead. Using either width directly as the side length overstates volume by three to four times.
Getting to real water volume
The formula gives the geometric volume of the tank to the rim. Three things make the real water volume smaller, and the calculator above lets you account for two of them directly:
- Fill height. Most tanks run an inch or two below the rim. Enter the actual water line and the result scales to match.
- Substrate. Gravel and sand sit in the water column. The substrate option removes the solid fraction of the bed (62 percent of its depth for typical gravel) from the total.
- Rock, wood and equipment. Use the displacement calculator to subtract hardscape by weight and equipment by type.
Water weight
Fresh water weighs about 8.34 pounds per US gallon (1 kg per litre). Reef water at a specific gravity of 1.025 is about 8.55 pounds per gallon. The calculator shows both so you can check what your stand and floor will carry before adding glass, substrate and rock on top.