Tank Volume Explained: Cylinders, Rectangular Tanks, and Fish Tanks

A tank’s volume is the amount of liquid it can hold, and for the shapes tanks actually take, it is one formula each: a cylinder is the circular area times the height, a rectangle is length times width times height, a sphere is four-thirds pi times the radius cubed. The arithmetic is easy. The mistakes are in the units, in measuring the inside rather than the outside, and in forgetting that a tank is never filled to the brim. This guide explains the formulas, the conversions between litres, gallons, and cubic metres, the difference between total and usable capacity, and the checks that keep a fish tank, a rainwater tank, and a fuel tank from being ordered in the wrong size. It builds only from tank-specific geometry; general volume conversions belong to the volume calculator, which is linked below.

The shapes: cylinders, rectangles, spheres, and cones

The vertical cylinder is the commonest tank shape, and its volume is the area of its circular base times its height. The base area is pi times the radius squared, and the radius is half the diameter — the mistake that halves or quarters the answer is using the diameter as the radius, which quadruples the volume. Worked example: a cylinder with an inside diameter of 1 metre, so a radius of 0.5 metres, and a height of 1.2 metres. The volume is π × 0.25 × 1.2, which is about 0.942 cubic metres, or about 942 litres.

A horizontal cylinder — a tank lying on its side — has the same total volume, but the volume at a given fill depth is a circular-segment calculation, not a simple proportion of the height. A tank half full by depth is not half full by volume: the segment at the bottom holds less than the segment at the middle, because the cross-section is widest at the centre. The calculator handles the partial-fill case; a ruler measurement of depth in a horizontal tank must not be read as a percentage of capacity.

Rectangular tanks are the simplest: length times width times height, all measured inside. A tank 2 metres long, 1 metre wide, and 0.8 metres deep holds 1.6 cubic metres, or 1,600 litres. Spheres hold four-thirds pi times the radius cubed, and cones hold one-third pi times radius squared times height — the cone is a third of the cylinder with the same base and height, which is a useful check. Irregular tanks, with sloped bottoms or internal baffles, need to be measured in sections and added, or filled and measured, because no single formula covers them.

Try the method on your own figures with the Tank Volume Calculator.

Units: litres, gallons, and cubic metres

Volume units are the commonest source of error in tank calculations, because three systems are in everyday use and two gallons exist. One cubic metre is 1,000 litres exactly. One US gallon is 3.785 litres, so a cubic metre is 264.17 US gallons. One imperial gallon is 4.546 litres, so a cubic metre is 219.97 imperial gallons. A US gallon and an imperial gallon differ by about 20%, and a tank ordered in the wrong gallon is a tank ordered in the wrong size.

Dimensions need the same care. A tank measured in feet and inches must be converted to a single unit before multiplying: 4 feet 6 inches is 4.5 feet, not 4.6, and a tank 4 feet by 2 feet by 2 feet holds 16 cubic feet, which is about 453 litres, or about 120 US gallons. The calculator accepts the common units and converts consistently, but a hand calculation must convert first, multiply second, and check the magnitude last: a result in the wrong order of magnitude is almost always a unit error, not a formula error.

Weight follows from volume and density, and it matters for any tank that stands on a floor or a stand. Water weighs 1 kilogram per litre, so a 1,600-litre tank weighs 1,600 kg full, plus the tank itself — over a tonne and a half, on the footprint of a large table. A fish tank, a rainwater tank, and a storage tank all need a floor and a stand rated for the full weight, not the empty weight, and the weight must be spread over the footprint, not concentrated on four small feet.

Usable capacity: freeboard, substrate, and fittings

No tank is filled to the brim. The unfilled space at the top, the freeboard, prevents overflow from sloshing, thermal expansion, and the displacement of anything put into the tank. A freeboard of 5 to 10% of the height is a common allowance for storage tanks, and it should be subtracted from the total volume to give the usable capacity: a 1,000-litre tank with 10% freeboard holds 900 litres in use.

Fish tanks lose more. Substrate on the bottom, rocks, driftwood, and equipment displace water, and the water level is kept below the rim for the fish’s safety and the owner’s floor. A tank rated at 200 litres may hold 160 to 180 litres of water in practice, depending on the aquascape, and the stocking and filtration calculations should use the water volume, not the rated volume. Measure the water depth after filling, with the substrate and decorations in place, for the figure that matters.

Fittings displace volume too, in both directions. An internal filter, a heater, and a pump occupy space inside the tank, reducing the water volume. An external sump adds volume outside it, increasing the total system volume. For a fuel or chemical tank, expansion space is a safety requirement, not a convenience: a tank filled to the brim on a cool morning can overflow by afternoon as the liquid warms and expands, and the ullage — the vapour space — is specified for that reason.

Choosing and checking a tank

Start from the need, in litres, and work backwards to the dimensions that fit the space. A rainwater tank is sized by roof area, rainfall, and the demand between rains. A fish tank is sized by the species and the number of fish, with the water volume, not the glass size, as the input. A storage tank is sized by the delivery interval and the consumption rate, with a margin for a missed delivery. In each case, the volume is the answer to a question about use, and the dimensions follow from it.

Check the result three ways: by the formula, by the unit conversion, and by sense. A tank 1 metre by 1 metre by 1 metre holds 1,000 litres — a tonne of water — and any tank near that size should give an answer near that figure, scaled by its dimensions. A result of 100 litres or 10,000 litres for a tank of that order is a decimal error, and it is cheaper to find it on paper than after delivery.

Finally, measure the tank itself, inside, before trusting a label. Manufacturers quote nominal sizes, and the inside dimensions — after wall thickness, after the base, after any internal structure — are smaller than the outside ones. A 5% difference in each dimension is a 14% difference in volume, which is the difference between a tank that fits the plan and one that overflows it.

Frequently asked questions