Quick answer
A bow front holds more than a rectangle with the same length, back-to-front flat depth and height. The extra is a half-ellipse worth π ÷ 4 of a strip the length of the tank and as wide as the bow depth. On a 36-inch tank with a 4-inch bow that is close to 10 gallons.Shape differences
A rectangle has four flat panels meeting at right angles. A bow front keeps the flat back and sides but replaces the front with a curved panel that bulges outward. From above, the rectangle is a box and the bow front is a box with a D-shaped addition on the front.
Measurement differences
Both need length and height. The rectangle needs a single width. The bow front needs two depth measurements: the flat depth at the corners, and the extra bow depth at the centre of the curve.
Formula differences
Rectangle: V = L × W × H. Bow front: V = L × D × H + π × (L ÷ 2) × B × H ÷ 2. Set B to zero and the bow front formula collapses to the rectangle.
Which calculator should you use?
Look at the front glass from above. If it is flat, use the rectangular calculator. If it curves, even slightly, use the bow front calculator and measure the bow depth; using the rectangle formula with the centre depth overstates volume and using it with the corner depth understates it.
Example comparison
36 × 12 × 20 in rectangle
37.4 gal (141.6 L)
36 in bow front, 12 in flat depth, 4 in bow, 20 in tall
47.2 gal (178.6 L)
The 4-inch bow adds 9.8 gallons, about 26% more water than the flat-front tank.