The two half circles combine into a single full circle, so the volume is a cylinder plus a box. Overall length must be at least the width, or the straight section would be negative.
How to measure a round end tank
- Measure overall length from the tip of one curve to the tip of the other.
- Width is the inside measurement across the straight section; it is also the diameter of the end curves.
- If the ends are shallower than full semicircles, the tank is closer to a rectangle with bowed ends and this formula will slightly overstate volume.
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.
Round End volume formula
V = ((L − W) × W × H) + (π × (W/2)² × H)
The two semicircular ends together form one full circle of diameter W. The straight middle section is length minus width. Multiply both by height and add.
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: Overall Length 60 inWidth 24 inHeight 24 in
Straight section: (60 − 24) × 24 × 24 = 20,736 in³. Ends: π × 12² × 24 = 10,857 in³. Total 31,593 in³ = 136.8 US gallons (517.7 litres).
Round end versus bullnose
Compared with a bullnose of the same overall dimensions, a round end tank gives up the corners at the second end, which is (1 − π ÷ 4) × (W/2)² × H of water. On a 24-inch-wide tank that is roughly 3 gallons per 24 inches of height. Against a plain rectangle, the stadium shape gives up that amount at both ends.
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.