metric capacity
RecommendedTank Capacity Comes From Shape and Internal Dimensions
Every tank volume is a shape formula followed by a unit conversion. The shape formula gives cubic feet or cubic metres. The conversion turns that into the unit actually needed, which for most US work is gallons.
- 1 cubic foot = 7.48 US gallons
- 1 cubic metre = 264.17 US gallons
- 1 US gallon of water weighs 8.34 lb
Vertical cylinderpi x radius squared x height = volume
Radius is half the internal diameter. A tank quoted as 6 ft diameter has a 3 ft radius.
Rectangular tankLength x width x height = volume
The simplest case, and the one where measurement error rather than arithmetic causes most mistakes.
Measure Internal, Not External
Tank capacity is the space inside the walls. Every published dimension is worth checking, because catalogue figures are frequently external and wall thickness is not always trivial.
On a thin walled steel tank the difference is small. On a rotomoulded polyethylene tank with half inch walls, or a concrete cistern with 6 inch walls, the difference is large. A concrete tank measuring 8 ft by 8 ft by 6 ft externally with 6 inch walls and floor has internal dimensions of 7 ft by 7 ft by 5.5 ft. That is 384 cubic feet against 269.5 cubic feet, a 30 percent overstatement.
Where the inside cannot be reached, subtract twice the wall thickness from each external width and diameter, and subtract the floor and lid thickness from the height. Measure the diameter at the widest point on a cylinder, and take two readings at right angles, because tanks go out of round.
Partial Fill on a Horizontal Cylinder
A horizontal cylinder is the case that trips people up. Volume does not rise in proportion to depth. A horizontal tank filled to half its diameter holds exactly half its capacity, but filled to a quarter of its diameter it holds far less than a quarter, because the cross section near the bottom is narrow.
The cross section of the liquid is a circular segment, and the volume is that segment area multiplied by the tank length.
Horizontal cylinder, partial fillSegment area = radius squared x (angle in radians minus the sine of that angle) divided by 2, then multiply by tank length
The angle is 2 x arccos((radius minus fill depth) divided by radius). A dipstick reading alone is not proportional to volume on a horizontal tank.
The practical consequence is that a fuel or water dipstick on a horizontal tank needs a calibrated chart, not evenly spaced marks. A 500 gallon horizontal tank at 25 percent of its diameter holds roughly 96 gallons, not 125.
Capsule and Oval Tanks
Capsule tanks
A capsule is a cylinder with hemispherical ends. Calculate it as a cylinder of the straight side length, then add one complete sphere of the same radius, since two hemispheres make one sphere.
Capsule tankpi x radius squared x straight length, plus 4 divided by 3 x pi x radius cubed
Use only the straight cylindrical section for the length. Including the domed ends in that length double counts them.
Oval tanks
An oval, or stadium shaped, tank has a cross section made of a rectangle with a half circle on each side. Calculate the cross section area, then multiply by the tank length.
Oval tankCross section = (width x height) minus the corner area, computed as rectangle plus one full circle of the end radius, then multiply by length
In practice: area equals (height minus width) x width, plus pi x (width divided by 2) squared, when the ends are semicircles of half the width.
Formulas by Shape
Tank shapeVolume formulaWatch for
Vertical cylinderpi x radius squared x heightUse internal radius, and fill height not tank height
Horizontal cylinder, fullpi x radius squared x lengthSame as vertical, just laid down
Horizontal cylinder, partialCircular segment area x lengthVolume is not proportional to depth
RectangularLength x width x heightSubtract wall thickness on all sides
CapsuleCylinder of straight length plus one sphereDo not include domes in the straight length
OvalCross section area x lengthCross section is a rectangle plus one full circle
Cone bottomCylinder plus one third x pi x radius squared x cone heightCone height is vertical, not slant length
Weight Is a Structural Problem
Water weighs 8.34 lb per US gallon. This is the number that turns a volume calculation into a load calculation, and it is regularly overlooked.
- A 275 gallon tote of water weighs about 2,294 lb plus the container, roughly the weight of a small car concentrated on a 4 ft by 3.5 ft footprint.
- A 500 gallon tank holds about 4,170 lb of water.
- A 1,000 gallon cistern holds about 8,340 lb, over 4 tons.
- A 50 gallon rain barrel holds about 417 lb, enough to matter on a wooden deck or a stand.
Anything denser than water is heavier still. Diesel is around 7.1 lb per gallon, so lighter, but many chemicals and slurries run at specific gravities of 1.2 to 1.8, which multiplies the load correspondingly. Check the floor, stand or platform rating before siting a tank, and check point loading, since a tank on legs concentrates the entire weight onto four small pads.
Full is the design caseSize the base, stand and restraints for the tank completely full, not for normal working level. Tanks get overfilled, and a stand that only works at half capacity is a stand that fails eventually.
Practical Checks
- Usable capacity is less than geometric capacity. Outlets sit above the floor, and freeboard is left at the top, so a nominal 1,000 gallon tank may deliver 900 usable gallons.
- Verify with a known volume. Adding a measured 50 gallons to an empty tank and marking the level gives a real calibration point that beats any formula.
- Round conservatively. Under-estimate capacity when sizing supply, and over-estimate it when sizing containment or secondary bunding.