How to Calculate Tank Volume

The basic idea

Every tank-volume formula comes down to the same principle: find the area of the tank's cross-section, then multiply by the dimension that runs perpendicular to it. For an upright cylinder, that is the circular base area times the height. For a tank lying on its side, it is the cross-section area times the length. Once you have the total volume in cubic units, you convert to gallons or litres.

Throughout this guide, volume is computed from internal dimensions and ideal geometry. Real tanks have wall thickness, fittings, and tolerances that make the true capacity slightly different, so treat the results as close estimates.

Vertical cylinder

A cylinder standing upright on its circular base has volume equal to the base area times the height: V = π × r² × h, where r is the radius and h is the height. To find a partial fill, replace h with the depth of liquid f: V = π × r² × f. Because the cross-section is the same at every height, the fill rises in direct proportion to volume.

Horizontal cylinder

A cylinder lying on its side has the same total volume, V = π × r² × L, but partial fill is more involved because the liquid forms a circular segment. The filled cross-section area uses the segment formula A = ½ × r² × (θ − sin θ), where θ = 2 × arccos((r − f) / r) and f is the depth of liquid. Below the halfway point you compute the filled segment directly; above it you compute the empty segment at the top and subtract from the total. The volume is that area times the length.

Rectangular (box) tank

A rectangular tank is the simplest: V = length × width × height. For a partial fill, replace the height with the liquid depth: V = length × width × f.

Capsule tank

A capsule is a cylinder with a hemisphere on each end. The two hemispheres together make one full sphere, so the total volume is the cylinder plus a sphere: V = π × r² × a + (4/3) × π × r³, where a is the length of the cylindrical middle section. Partial fill combines a spherical cap for the rounded ends with the cylinder math for the middle.

Oval (stadium) tank

An oval or "obround" tank has a stadium-shaped cross-section — a rectangle with a semicircle on each side. Its cross-section area is the circle area plus the straight middle band, and the volume is that area times the length. Partial fill is computed by combining the circular-segment math with the rectangular middle section.

True elliptical tank

A true horizontal elliptical cross-section tank has volume V = (π × width × height × L) / 4. This is different from a cylindrical tank fitted with 2:1 elliptical or dished heads, which is a separate construction; this guide and our calculator treat the true-ellipse cross-section.

Cone and frustum tanks

A truncated cone (frustum) has volume V = (π × h / 3) × (R₁² + R₁R₂ + R₂²), where R₁ and R₂ are the top and bottom radii. Cone-bottom and cone-top tanks combine a cylinder with a cone section; the difference between them is fill order — a cone-bottom tank fills the cone first, while a cone-top tank fills the cylinder first.

Converting to gallons and litres

Once you have a volume in cubic units, convert with standard factors: one US gallon is 231 cubic inches, one cubic foot is about 7.48 US gallons, and one US gallon is about 3.785 litres. Our calculator shows results in US gallons, imperial gallons, litres, cubic feet, and cubic metres at once, so you do not have to convert by hand.

Try it yourself

Rather than working the formulas manually, you can enter your tank's dimensions into the tank volume calculator, which handles all ten shapes including partial fill. For the exact formulas, constants, and the sources behind them, see the methodology page.

Note: These formulas assume ideal geometry and internal dimensions. They do not account for wall thickness, fittings, baffles, tilt, or manufacturing tolerances, so results are close estimates rather than exact capacities.