Tank Volume Calculator

Using the tank volume calculator

Choose the tank shape first, because the form shows only the measurements that shape needs. Enter each dimension with its own unit (millimetres up to yards), measured on the inside of the tank, since the liquid only occupies the interior.

The first block of results is the full capacity of the tank. If you also type a filled height (the depth of liquid measured from the lowest point of the tank), a second block shows the share of the tank that is filled and the volume of liquid in cubic metres, cubic feet, litres, US gallons, UK gallons and barrels.

A filled height taller than the tank is rejected. For a rectangular tank, a filled height equal to the tank height simply gives 100%.

Supported tank shapes

A capsule is a cylinder with a hemisphere on each end, and here the length or height you type is the straight cylindrical section only. The hemispheres add one full sphere, 4/3 π r³. Domes are treated as hemispheres with the same diameter as the tank, so a dome adds half a sphere and a height equal to the radius. An oblique cone has its tip off-centre, but its volume depends only on its base and its vertical height, so it equals that of a symmetric cone.

The two oval shapes are a rectangle capped by semicircles, the usual profile of an "oval" tank. For the horizontal version the cross-section is wider than it is tall; for the vertical version it is taller than it is wide. The tool tells you if the two dimensions are the wrong way round.

Worked examples

Rectangular water tank. The inside of a tank is 2 m wide, 3 m long and 1.5 m high. Capacity is 2 × 3 × 1.5 = 9 m³, which is 9,000 litres or about 2,377.5 US gallons. With the water 1.2 m deep, the filled share is 1.2 ÷ 1.5 = 80%, which is 7.2 m³ or 7,200 litres.

Horizontal cylinder. A fuel tank lies on its side with a 1.2 m diameter and a 3 m length. Its capacity is π × 0.6² × 3 = 3.393 m³, or 3,393 litres. When the liquid is 0.3 m deep, the cross-section of the liquid is a circular segment, not a rectangle, so the fill is not 0.3 ÷ 1.2 = 25%.

segment area = r² · arccos((r − h) ÷ r) − (r − h) · √(2 r h − h²)r is the tank radius and h the liquid depth. Multiply by the tank length to get volume.

With r = 0.6 m and h = 0.3 m the segment area is 0.36 × 1.0472 − 0.3 × 0.5196 = 0.2211 m². Times 3 m gives 0.663 m³, or 663 litres, which is 19.55% of the tank. A vertical cylinder is much simpler: liquid volume is just π r² times the depth.

Vertical tank with a conical outlet. A tank has a 2 m diameter, a 1.5 m straight section and a 0.8 m cone narrowing to a 0.2 m outlet. The cylinder holds π × 1² × 1.5 = 4.712 m³. The truncated cone holds π × 0.8 ÷ 3 × (1² + 1 × 0.1 + 0.1²) = 0.930 m³. Together that is 5.642 m³, or 5,642 litres.

Liquid inside the cone. Suppose that same tank holds liquid 0.4 m deep, measured from the outlet, so the surface is still inside the cone. The liquid itself is a truncated cone only 0.4 m tall, not 0.8 m. At the surface the cone has widened to a radius of ρ = 0.1 + (1 − 0.1) × 0.4 ÷ 0.8 = 0.55 m, so its volume is:

V = π × y ÷ 3 × (r² + r ρ + ρ²), with ρ = r + (R − r) × y ÷ hy is the liquid depth inside the cone, h the cone height, R and r the large and small radii. Once the level passes the top of the cone, y is replaced by h and the straight section adds π R² for every extra unit of depth.

With y = 0.4 m, r = 0.1 m and ρ = 0.55 m: π × 0.4 ÷ 3 × (0.01 + 0.055 + 0.3025) = 0.15394 m³, or about 154 litres. That is 2.73% of the 5.642 m³ capacity, even though the liquid already stands halfway up the cone. A pointed cone (the oblique and dome-top oblique versions) works the same way with r = 0, which reduces the volume to π R² y³ ÷ (3 h²): a cone half full by depth holds only one eighth of the cone.

Litres, gallons, barrels and cubic feet

The calculator converts litres with these exact definitions: 1 US gallon = 3.785411784 L, 1 UK (imperial) gallon = 4.54609 L, and 1 oil barrel = 42 US gallons = 158.987294928 L. One cubic foot is 28.316846592 L.

For other conversions, the volume converter covers many more units.

Getting an accurate answer

• Measure inside dimensions. Subtract the wall thickness from outside measurements, or the answer will be too high.
• Real tanks have fittings, baffles, domed or dished ends and sometimes slightly sloped floors. Treat results as a good estimate, not a certified capacity, and use the manufacturer's rating for legal or safety purposes.
• For the liquid level, measure from the true bottom of the tank, including any cone or dome at the base, with a dipstick or sight glass.
• Never fill a tank to its brim: leave room for expansion and for any overflow requirements that apply.

Simple shapes also have their own tools: the volume of a box and volume of a cylinder calculators, plus the aquarium volume calculator and the pool volume calculator. Cone and sphere formulas are explained in the cone volume and sphere volume calculators.