Tank Volume Calculator

How to calculate tank volume

The volume of a tank is the cross-sectional area of its shape multiplied by the dimension that runs along its length or height. The hard part is simply using the right area formula for the cross-section — a circle, a rectangle, an ellipse, a stadium (obround), or a cone — and being consistent with units. This calculator does that for ten common tank shapes and converts the result into every standard volume unit at once. For the derivations and the sources behind each formula, see the methodology page.

Formulas for each tank shape

Below, r is radius, d is diameter, L is length, h is height, w is width, and a is the straight side-wall length of a capsule. All dimensions are inside dimensions.

Vertical & horizontal cylinder

A cylinder’s volume is the circular end area times its length:

V = π × r² × L

Orientation does not change the total volume. It does change partial-fill behaviour: a vertical cylinder fills evenly with height, while a horizontal cylinder fills as a circular segment (explained below).

Rectangular / box tank

V = L × w × h

The simplest case — length times width times height. Partial fill is linear: half the height holds half the volume.

Capsule (vertical & horizontal)

A capsule is a cylinder with a hemispherical cap on each end. The two hemispheres together make one sphere, so:

V = π × r² × ( (4/3) × r + a )

Oval — stadium / obround (horizontal)

An oval tank here has a stadium-shaped cross-section: a rectangle capped by two semicircles. With semicircle radius r = h/2 and straight width a = w − h:

V = ( π × r² + 2 × r × a ) × L

True elliptical cross-section (horizontal)

A true elliptical tank has a cross-section that is a genuine ellipse with width w and height h. This is different from a stadium oval and from a cylinder with elliptical end-caps:

V = ( π × w × h × L ) / 4

Cone / frustum

A frustum is a cone with the tip cut off, with top radius R₁ and bottom radius R₂:

V = ( π × h / 3 ) × ( R₁² + R₁ × R₂ + R₂² )

Cone-bottom & cone-top tanks

These are a cylinder joined to a cone (frustum) section. The total volume is the cylinder plus the cone section. The two differ in how they fill: a cone-bottom tank fills the cone first and then the cylinder above it, while a cone-top tank fills the cylinder first and then the cone on top. The calculator accounts for this fill order.

Volume units explained

Results are shown in five units at once so there is no need to convert by hand. Petroleum barrels can be added with a checkbox.

Unit	Equal to	Notes
US gallon	≈ 3.785 litres	US liquid gallon
Imperial gallon	≈ 4.546 litres	UK gallon, ~20% larger than US
Litre	1,000 cm³	1 m³ = 1,000 litres
Cubic foot (ft³)	≈ 28.317 litres	≈ 7.481 US gallons
Cubic metre (m³)	1,000 litres	SI volume unit
Petroleum barrel	42 US gal ≈ 158.99 litres	Oil barrel — not the same as a 55-gallon drum

Note that a petroleum (oil) barrel is 42 US gallons, which is different from a 55-gallon steel drum (about 208 litres). They are often confused but are not the same.

Partial-fill volume and the horizontal cylinder

For a vertical tank, the filled volume is proportional to the liquid height — fill it halfway up and you have half the volume. A horizontal cylinder is different. The liquid forms a circular segment in the round cross-section, so the volume does not change evenly with depth: near the bottom and near the top, a change in depth adds relatively little volume, while near the middle it adds the most.

The filled area of the segment is calculated as:

A = ½ × r² × ( θ − sin θ ), where θ = 2 × arccos( (r − fill) / r )

Multiplying that area by the length gives the filled volume. The only point where a horizontal cylinder behaves “simply” is exactly half full, where it holds precisely half its total volume. This is why a sight gauge on a horizontal tank is not linear, and why dipstick-to-gallons charts (such as for heating-oil tanks) are curved rather than evenly spaced.

Frequently asked questions

How do I calculate the volume of a tank?

Pick the tank shape, enter its inside dimensions, and the calculator multiplies the cross-sectional area by the length or height. For a cylinder that is π × radius² × length; for a rectangular tank it is length × width × height. The result is shown in US gallons, imperial gallons, litres, cubic feet and cubic metres at once.

How do I work out the volume of a partially filled tank?

Turn on “Calculate partial fill” and enter the liquid level (the depth of liquid measured from the bottom). For a vertical tank the filled volume scales with height. For a horizontal cylinder the filled cross-section is a circular segment, so the relationship between depth and volume is not linear — the calculator handles this and reports filled and empty volumes separately.

What units does the calculator output?

Every result is shown in US gallons, imperial (UK) gallons, litres, cubic feet and cubic metres simultaneously, so you do not need to convert. Petroleum barrels (42 US gallons) can be shown as well by ticking the “Show petroleum barrels” box.

Is the US gallon the same as the imperial gallon?

No. One US liquid gallon is about 3.785 litres, while one imperial (UK) gallon is about 4.546 litres — roughly 20% larger. The calculator shows both so there is no ambiguity.

Does the calculator account for the tank wall thickness?

No. It computes the volume of an ideal geometric shape from the dimensions you enter. It does not account for wall thickness, internal fittings or baffles, tank tilt, deformation, or manufacturing tolerances. Enter inside dimensions for the closest estimate of liquid capacity.

What is the difference between an oval tank and an elliptical tank?

On this site an “oval (stadium)” tank has a cross-section made of a rectangle capped by two semicircles (an obround), while a “true elliptical” tank has a cross-section that is a genuine ellipse. They are different shapes with different volumes, so they are offered separately.