Skip to content

Reference

Aquarium Volume Formulas

Every formula used on this site, grouped by shape family. All dimensions are interior. The result is in cubic units of whatever you measured in; convert with the factors at the bottom.

The one rule behind every formula

Volume = floor area × height. Only the floor-area step changes from shape to shape. In inches, divide cubic inches by 231 for US gallons. In centimetres, divide cubic centimetres by 1,000 for litres.

Standard Tanks

Rectangular

V = L × W × H

Multiply the three interior dimensions. In inches, divide the result by 231 for US gallons. In centimetres, divide by 1,000 for litres.

Example: A 36 × 18 × 16 inch interior gives 10,368 cubic inches. Dividing by 231 gives 44.9 US gallons, or about 169.9 litres.

Open calculator →

Cube

V = S³

Cube the interior side length. A cube with 12-inch sides holds 1,728 cubic inches, which is exactly one cubic foot or 7.48 US gallons.

Example: A 12-inch cube is 12 × 12 × 12 = 1,728 cubic inches, which is 7.48 US gallons or 28.3 litres.

Open calculator →

Breeder

V = L × W × H

A breeder is a rectangular prism, so the standard box formula applies. The extra front-to-back width is what sets its volume apart from a regular tank of the same length.

Example: A 36 × 18 × 16 inch breeder is 10,368 cubic inches, which is 44.9 US gallons or 169.9 litres, noticeably more than its 40-gallon label.

Open calculator →

Shallow

V = L × W × H

Shallow tanks are rectangular prisms. Because the height is small, every inch of substrate or air gap is a large share of the total, so the adjustment options matter more here than on any other shape.

Example: A 24 × 14 × 9 inch shallow tank holds 3,024 cubic inches, or 13.1 US gallons (49.6 litres) to the rim. With a 1-inch gap and 2 inches of soil it drops to about 9 gallons.

Open calculator →

Curved Tanks

Bow Front

V = (L × D × H) + (π × (L/2) × B × H ÷ 2)

The tank is split into a rectangular box (length × flat depth) plus a half-ellipse whose semi-axes are half the length and the bow depth. Both are multiplied by height and added.

Example: Box: 36 × 12 × 20 = 8,640 in³. Bow: π × 18 × 4 × 20 ÷ 2 = 2,262 in³. Total 10,902 in³ = 47.2 US gallons (178.6 litres). The bow adds about 9.8 gallons.

Open calculator →

Cylinder

V = π × r² × H

Multiply the circular floor area (π times radius squared) by the height. If you measured the diameter, halve it before entering.

Example: π × 10² × 24 = 7,540 in³, which is 32.6 US gallons or 123.6 litres.

Open calculator →

Half Cylinder

V = π × r² × H ÷ 2

Half the volume of a full cylinder with the same radius and height. The radius is half the length of the flat back panel.

Example: π × 12² × 20 ÷ 2 = 4,524 in³, which is 19.6 US gallons or 74.1 litres.

Open calculator →

Elliptical

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.

Example: π × 15 × 9 × 20 = 8,482 in³, which is 36.7 US gallons or 139.0 litres.

Open calculator →

Bullnose

V = ((L − r) × W × H) + (π × r² × H ÷ 2)

The rectangular section runs from the flat end to the start of the curve (length minus radius). The rounded end is a half cylinder with the given radius. Both are multiplied by height and added.

Example: Box: (48 − 9) × 18 × 20 = 14,040 in³. Nose: π × 9² × 20 ÷ 2 = 2,545 in³. Total 16,585 in³ = 71.8 US gallons (271.8 litres).

Open calculator →

Round End

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.

Example: 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).

Open calculator →

Fish Bowl

V = π × d³ ÷ 6

The volume of a sphere. For a bowl with a flat base, the calculator removes the spherical cap below the base. Water height is measured from the inside floor and uses the spherical segment formula.

Example: A 10-inch bowl is π × 10³ ÷ 6 = 524 in³ as a full sphere, which is 2.27 US gallons or 8.6 litres. Filled to the usual level below the opening it holds closer to 1.9 gallons.

Open calculator →

Corner Tanks

Corner Bow Front

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.

Example: 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).

Open calculator →

Corner Cylinder

V = π × r² × H ÷ 4

A quarter of a full cylinder. The two straight sides that meet in the corner are both equal to the radius.

Example: π × 24² × 24 ÷ 4 = 10,857 in³, which is 47.0 US gallons or 177.9 litres.

Open calculator →

Corner Prism

V = ½ × a × b × H

A right triangle has half the area of the rectangle formed by its two legs. Multiply that area by the height.

Example: ½ × 24 × 24 × 20 = 5,760 in³, which is 24.9 US gallons or 94.4 litres.

Open calculator →

Polygon Tanks

Hexagon

V = (3√3 ÷ 2) × s² × H

A regular hexagon has area 2.598 × s². Multiply by height. The side length is the width of one of the six glass panels.

Example: 2.598 × 12² × 24 = 8,979 in³, which is 38.9 US gallons or 147.1 litres.

Open calculator →

Flat-Back Hexagon

V = (L × D − (L − F) × (D − S) ÷ 2) × H

Start with the full rectangle (back length × overall depth) and remove the two triangular corners cut off by the angled panels. Each triangle has legs (L − F) ÷ 2 and (D − S).

Example: Rectangle 36 × 18 = 648 in². Corners removed: (36 − 18) × (18 − 8) ÷ 2 = 90 in². Floor 558 in² × 20 = 11,160 in³ = 48.3 US gallons (182.9 litres).

Open calculator →

Octagon

V = 2 × (1 + √2) × s² × H

A regular octagon has area 4.828 × s². Multiply by height.

Example: 4.828 × 10² × 24 = 11,588 in³, which is 50.2 US gallons or 189.9 litres.

Open calculator →

Pentagon

V = (√(25 + 10√5) ÷ 4) × s² × H

A regular pentagon has area 1.720 × s². Multiply by height.

Example: 1.720 × 12² × 20 = 4,954 in³, which is 21.4 US gallons or 81.2 litres.

Open calculator →

Custom Shapes

L-Shaped

V = (L1 × W1 + L2 × W2) × H

Split the L into two rectangles that do not overlap, add their floor areas and multiply by the common height.

Example: Section 1: 60 × 24 = 1,440 in². Section 2: 36 × 24 = 864 in². Floor 2,304 in² × 24 = 55,296 in³ = 239.4 US gallons (906.2 litres).

Open calculator →

Trapezoid

V = ½ × (B1 + B2) × D × H

Average the two parallel bases, multiply by the perpendicular depth for the floor area, then multiply by height.

Example: ½ × (36 + 18) × 18 = 486 in² floor. × 20 = 9,720 in³ = 42.1 US gallons (159.3 litres).

Open calculator →

Floor-area comparison

Area of the footprint for a characteristic dimension s, relative to a square with side s.

ShapeFloor areaRelative to s²
Square (s = side)s²1.000
Circle (s = diameter)π × s² ÷ 40.785
Hexagon (s = side)2.598 × s²2.598
Octagon (s = side)4.828 × s²4.828
Pentagon (s = side)1.720 × s²1.720
Right triangle (s = each leg)s² ÷ 20.500
Quarter circle (s = radius)π × s² ÷ 40.785
Sphere (s = diameter, volume)π × s³ ÷ 60.524

Unit conversion

  • Cubic inches ÷ 231 = US gallons
  • US gallons × 3.785 = litres
  • Cubic centimetres ÷ 1,000 = litres
  • Litres ÷ 3.785 = US gallons
  • Cubic feet × 7.48 = US gallons

Use the unit converter for anything else.

Frequently asked questions

After. Multiply the three measurements in the unit you measured, then convert the cubic result. Mixing inches and centimetres in one calculation gives nonsense.
Because all these tanks have vertical walls, so the floor area is the same at every height. Volume at a lower water line is the full volume times the height ratio. The fish bowl is the exception and uses spherical segment geometry.
Exact for the ideal shape. Real tanks deviate through glass thickness, slightly off-square corners and curved panels that are arcs rather than true ellipses, usually within one or two percent.