The floor area is the average of the two parallel widths times the perpendicular depth, exactly as if the tank were a rectangle of average width.
How to measure a trapezoid tank
- Measure the inside width of the front panel and the back panel.
- Depth is the straight perpendicular distance between those two panels, not the length of the angled sides.
- If the two sides are not symmetric the formula still works, as long as the front and back are parallel.
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.
Trapezoid volume formula
V = ½ × (B1 + B2) × D × H
Average the two parallel bases, multiply by the perpendicular depth for the floor area, then 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: Front Base 36 inBack Base 18 inDepth (front to back) 18 inHeight 20 in
½ × (36 + 18) × 18 = 486 in² floor. × 20 = 9,720 in³ = 42.1 US gallons (159.3 litres).
A trapezoid is an averaged rectangle
Because the width changes linearly from back to front, the trapezoid holds exactly what a rectangle of the average width would hold. A 36-inch front and 18-inch back behave like a 27-inch-wide rectangle. This also means substrate and fill-height adjustments scale the same way they do on a box tank.
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.