Bow-front aquarium volume calculator
Measure the length, the depth at the ends and at the center of the bow, and the height. The bow is calculated as a true circular arc.
Bow-front volume formula
A bow-front tank is a rectangle plus a curved front. Seen from above, the curve is a circular segment whose chord is the tank length L and whose height (sagitta) is the extra depth at the center, s = center depth − end depth.
radius r = (L²/4 + s²) ÷ 2s, angle θ = 2 × asin(L ÷ 2r), segment area = r²/2 × (θ − sin θ).
volume = (L × end depth + segment area) × height, then ÷ 231 for US gallons (inches) or ÷ 1,000 for liters (cm).
Worked example
A popular "46-gallon bow-front" measures 36 × 16.5 × 20 inches, with about 12 inches of depth at the ends. The bow adds s = 4.5 inches; the arc radius is 38.25 inches and the segment area is about 109 square inches. The footprint is 432 + 109 = 541 square inches, times 20 inches of height = 10,827 cubic inches, or 46.9 US gallons (177 liters) to the rim.
Why not just average the depths?
Averaging the end and center depths treats the bow as a straight-sided trapezoid and underestimates the volume. Using the center depth for the whole tank overestimates it. A shallow arc is very close to a parabola, whose area is two-thirds of the bounding rectangle — the exact arc formula above confirms this and handles deeper bows too.
FAQ
How many gallons is a 36-inch bow-front tank?
A 36 × 16.5 × 20 inch bow-front with 12-inch ends holds about 46.9 gallons to the rim, which is why it is sold as a 46-gallon tank.
Where do I measure the depth of a bow-front tank?
Measure front to back at one end (the shallowest point) and again at the middle of the bow (the deepest point), both on the outside.