Aquarium Volume Formulas
This reference covers the volume formula for every aquarium shape in common use. Because tank shapes range from simple boxes to cylinders, polygons, and compound curves, no single formula applies to all tanks. Using the wrong formula can produce errors of 10–30%, which translates directly into incorrect dosing, overstocking, and equipment mismatches. Every formula below assumes accurate interior measurements — if you have not measured your tank yet, start with how to measure aquarium volume. Each section below shows the formula, explains the variables, and links to the interactive calculator for that shape.
Basic Volume Formula
All volume calculations begin with the same concept: multiply the cross-sectional area of the tank by its height. For a rectangular tank, the cross section is simply length × width, giving the familiar three-factor formula.
V = L × W × H
- L — Inside length (longest horizontal dimension)
- W — Inside width (front to back)
- H — Fill height (bottom to water line)
If measured in inches: divide the product by 231 to get US gallons.
If measured in centimeters: divide by 1,000 to get liters.
For definitions of inside dimensions, fill height, nominal volume, and other terms used throughout these formulas, see the aquarium volume glossary.
Standard Tank Formulas
Standard tanks share the rectangular prism shape. The formulas are identical; only the proportions differ between tank types.
Rectangular Aquarium
V = L × W × H
Measure the inside dimensions of your rectangular tank from glass to glass, not including the frame or trim. For length, measure the longest horizontal edge; for width, measure front to back; for height, measure from the inner bottom to the desired water line.
Cube Aquarium
V = S³
Measure any one inside edge of the cube from glass panel to glass panel. All three dimensions should be identical; if they differ slightly, use the rectangular calculator instead for a more accurate result.
Breeder Aquarium
V = L × W × H
Measure inside dimensions just like a standard rectangular tank. Breeder tanks are distinguished by a width-to-height ratio greater than 1:1. If your tank is taller than it is wide, it is likely a standard rather than a breeder.
Shallow Aquarium
V = L × W × H
Measure the interior length, width, and height from the inside glass surfaces. Shallow tanks typically have a height under 12 inches. Include only the water-filled portion when calculating volume; do not include any exposed land area in a paludarium.
Curved Tank Formulas
Curved tanks require formulas derived from circular geometry. The key variable for all circular shapes is the radius (half the inside diameter). Bow front tanks combine a rectangular section with a half-ellipse; fish bowls use the full sphere formula.
Bow Front Aquarium
V = (L × D × H) + (π × (L÷2) × B × H) ÷ 2
Measure the straight back panel for the flat depth. For the bow depth, measure from the plane of the back glass to the furthest point of the curved front panel, then subtract the flat depth. The length is measured along the back panel from side to side.
Cylindrical Aquarium
V = π × r² × H
Measure the inside diameter of the cylinder at the widest point and divide by two to get the radius. For acrylic cylinders, be sure to measure inside the wall, not outside. Height is measured from the interior bottom to the water line.
Half Cylinder Aquarium
V = (π × r² × H) ÷ 2
Measure from the flat back wall of the tank to the outermost point of the curved front to get the radius. Alternatively, measure the full width of the flat back panel and divide by two. Height is measured inside from bottom to water line.
Elliptical Aquarium
V = π × a × b × H
Measure the longest inside diameter and divide by two for the semi-major axis. Then measure the shortest inside diameter (perpendicular to the first) and divide by two for the semi-minor axis. Height is inside bottom to water line.
Bullnose Aquarium
V = ((L - r) × W × H) + (π × r² × H) ÷ 2
Measure overall length from the flat end to the farthest point of the curved end. The bullnose radius is the distance from the center of the curve to the curved glass surface. Width is measured across the flat sides. Height is inside from bottom to water line.
Round End Aquarium
V = ((L - W) × W × H) + (π × (W÷2)² × H)
Measure the total inside length from the outermost curve on one end to the other. Width is the inside distance between the two long flat sides, which also equals the diameter of each semicircular end cap. Height is inside bottom to water line.
Fish Bowl
V = (π × d³) ÷ 6
Measure the widest inside diameter of the bowl from one inner wall to the opposite inner wall. For bowls with a flat bottom, measure at the widest horizontal cross-section, not at the base. Note that actual water volume will be less than the full sphere because bowls have an open top.
Corner Tank Formulas
Corner tanks are designed to fit 90-degree room corners. The corner prism is a right-triangle prism with exactly half the volume of a rectangle using the same two wall-facing dimensions. Corner cylinders and corner bow fronts combine circular geometry with the corner placement constraint.
Corner Bow Front Aquarium
V = (L × D × H) + (π × (L÷2) × B × H) ÷ 2
Place a straight edge across the back corner to define the flat depth plane. Measure the bow depth from that plane to the outermost point of the curve. Length is measured along the straight back edge where the two wall-facing panels meet.
Corner Cylinder Aquarium
V = (π × r² × H) ÷ 4
Measure along either flat back panel from the corner to the edge where the curve begins; this distance is the radius. Both flat panels should be equal in length. Height is measured inside from the bottom to the water surface.
Corner Aquarium
V = ½ × a × b × H
Measure the inside length of each back panel that rests against the wall. These are the two legs of the right triangle. They do not need to be equal. Height is measured inside from the bottom to the waterline. The diagonal front panel length is not needed for the volume calculation.
Polygon Tank Formulas
Polygon tanks — hexagonal, octagonal, and pentagonal — use regular polygon area formulas. All sides of a regular polygon are equal, so a single side length measurement is all that is needed. The cross-sectional area is multiplied by height to get volume.
Hexagonal Aquarium
V = (3√3 ÷ 2) × s² × H
Measure the inside length of any one of the six identical flat panels. All sides of a regular hexagon are equal, so a single measurement is sufficient. If the sides are unequal, the tank is not a true hexagon and this formula will be approximate.
Octagon Aquarium
V = 2(1 + √2) × s² × H
Measure the inside length of any one of the eight identical panels. For accuracy, confirm that all eight sides are equal. If your tank has alternating long and short sides, it is not a regular octagon and this formula will not apply exactly.
Pentagon Aquarium
V = (√(25 + 10√5) ÷ 4) × s² × H
Measure the inside length of one of the five equal panels. Verify that all five sides are the same length. The pentagon formula assumes a regular pentagon; irregular five-sided tanks would need to be decomposed into simpler shapes for calculation.
Custom Tank Formulas
Custom shapes like L-shaped and trapezoid tanks require decomposing the footprint into simpler geometric sections. L-shaped tanks use two non-overlapping rectangles; trapezoid tanks use the average of the two parallel sides multiplied by depth.
L-Shaped Aquarium
V = (L1 × W1 × H) + (L2 × W2 × H)
Divide the L-shape into two non-overlapping rectangles. Measure the inside length and width of each rectangle separately. Both sections must share the same height. Be careful not to double-count the overlapping corner area where the two sections meet.
Trapezoid Aquarium
V = ½(b1 + b2) × D × H
Measure the inside length of the front panel (base 1) and the inside length of the back panel (base 2). Depth is the perpendicular distance between these two parallel panels measured inside. Height is inside from the bottom to the water line.
Formula Comparison Table
Quick reference for all shapes showing the formula pattern and the measurements you need to collect before calculating. For standard tank dimensions across the most common nominal sizes, see aquarium volume by size.
| Shape | Formula Pattern | Inputs Needed |
|---|---|---|
| Rectangular / Breeder / Shallow / Cube | L × W × H | Length, Width, Height |
| Cylinder | π × r² × H | Radius, Height |
| Half Cylinder | (π × r² × H) ÷ 2 | Radius, Height |
| Corner Cylinder | (π × r² × H) ÷ 4 | Radius, Height |
| Elliptical | π × a × b × H | Semi-major axis, Semi-minor axis, Height |
| Bow Front | (L × D × H) + (π × (L÷2) × B × H) ÷ 2 | Length, Flat Depth, Bow Depth, Height |
| Bullnose | ((L − r) × W × H) + (π × r² × H) ÷ 2 | Length, Width, Radius, Height |
| Round End | ((L − W) × W × H) + (π × (W÷2)² × H) | Length, Width, Height |
| Fish Bowl | (4÷3) × π × r³ | Radius |
| Hexagon | (3√3 ÷ 2) × s² × H | Side length, Height |
| Octagon | 2(1 + √2) × s² × H | Side length, Height |
| Pentagon | (√(25 + 10√5) ÷ 4) × s² × H | Side length, Height |
| Corner Prism | ½ × a × b × H | Leg 1, Leg 2, Height |
| L-Shaped | (L1 × W1 × H) + (L2 × W2 × H) | Section 1 L&W, Section 2 L&W, Height |
| Trapezoid | ½(b1 + b2) × D × H | Front base, Back base, Depth, Height |
Unit Conversion
Every formula above produces cubic units — either cubic inches (when measuring in inches) or cubic centimeters (when measuring in centimeters). Convert to practical volume units using these divisors:
Cubic Inches → US Gallons
Gallons = in³ ÷ 231
The US gallon is legally defined as exactly 231 cubic inches. This definition dates to the British wine gallon of 1707 and equals approximately 3.785 liters.
Cubic Centimeters → Liters
Liters = cm³ ÷ 1,000
One liter is exactly 1,000 cubic centimeters (also equal to one milliliter × 1,000). This makes metric calculations especially clean when all dimensions are in centimeters.
Converting liters to gallons: divide by 3.785411784. For example, 200 L ÷ 3.785 = 52.8 gal.
Use our aquarium volume unit converter to convert between all six volume units instantly. International fishkeepers working in centimetres and litres can find a metric-first formula reference and size table on the aquarium volume in litres page.
To apply any of these formulas without doing the arithmetic yourself, use the free aquarium volume calculator.