The calculator treats the footprint as a right-angled triangle whose hypotenuse is the front span, plus a half-ellipse that bulges outward from that hypotenuse by the bow depth.
How to measure a corner bow front tank
- Front span: stretch a tape in a straight line from the outer end of one wall side to the outer end of the other.
- Bow depth: measure from the middle of that straight line out to the inside of the curved glass.
- The two wall sides should be equal; if they are not, the formula is an approximation.
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.
Corner Bow Front volume formula
V = (S² ÷ 4 + π × S × B ÷ 4) × H
The footprint is a right triangle between the two wall sides (area S² ÷ 4 when the front span S is the hypotenuse) plus a half-ellipse bulge with semi-axes S ÷ 2 and bow depth B.
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 Span 36 inBow Depth 6 inHeight 24 in
Triangle: 36² ÷ 4 = 324 in². Bulge: π × 36 × 6 ÷ 4 = 170 in². Area 494 in² × 24 = 11,852 in³ = 51.3 US gallons (194.2 litres).
What the corner bow front formula assumes
The triangle term assumes the two wall sides meet at a right angle and are equal in length, which makes the span the hypotenuse of an isosceles right triangle. Setting bow depth to zero gives a plain corner prism. Setting bow depth to about 0.29 times the span reproduces a quarter circle, at which point the corner cylinder calculator is the better model.
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.