Measure one panel and the height. If the panels are not all equal, as on many corner pentagons, treat the tank as a trapezoid or a corner prism with a cut corner instead.
How to measure a pentagon tank
- Measure the inside width of one panel between seams.
- Face-to-face is not defined on a pentagon; vertex-to-opposite-face width is 1.539 × side.
- For a corner pentagon with two long wall sides and three shorter front panels, this formula does not apply.
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.
Pentagon volume formula
V = (√(25 + 10√5) ÷ 4) × s² × H
A regular pentagon has area 1.720 × s². Multiply by height.
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 20 in
1.720 × 12² × 20 = 4,954 in³, which is 21.4 US gallons or 81.2 litres.
Pentagon versus hexagon efficiency
With the same panel width, a pentagon has 66% of a hexagon's floor area and fills only 76% of its circumscribed circle, compared with 83% for a hexagon. Five-sided tanks are chosen for their look rather than their volume efficiency.
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.