Measure the longest inside width and the shortest inside width, halve each, and enter them as the two semi-axes. A true stadium shape with straight sides between two semicircles should use the round end calculator instead.
How to measure a elliptical tank
- Measure the long diameter across the widest part of the tank and divide by two for a.
- Measure the short diameter at right angles to it, through the centre, and divide by two for b.
- If the sides are straight for part of their length, the tank is a round end (stadium) shape, not an ellipse.
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.
Elliptical volume formula
V = π × a × b × H
The floor of an oval tank is an ellipse with area π × a × b, where a and b are half the long and short diameters. 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: Semi-Major Axis (a) 15 inSemi-Minor Axis (b) 9 inHeight 20 in
π × 15 × 9 × 20 = 8,482 in³, which is 36.7 US gallons or 139.0 litres.
Elliptical versus cylinder volume
For a fixed long diameter, flattening a circle into an ellipse removes volume in direct proportion to the short axis. An oval that is 30 inches long and 18 inches wide holds 60% of the volume of a 30-inch round tank of the same height. That makes ovals a good way to get a long viewing face in a narrow room.
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.