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How to Calculate Tank Volume

The volume of a tank is the area of its cross-section multiplied by its length or height. This guide walks through the formulas for each common tank shape and how to handle a tank that is only partially full.

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.

How to calculate a partially full tank

A full tank uses its total internal height or length. To find the volume of a partially full tank, you instead use the liquid level — the fill height measured from the bottom of the tank. Converting that liquid level to volume depends heavily on the tank's shape.

Rectangular and vertical cylindrical tanks are simple. Their cross-section is the same at every level, so partially filled tank volume rises linearly with liquid depth — double the depth and you double the volume. Just replace the full height with the fill height in the formula, as on the rectangular tank volume calculator and the vertical cylindrical tank volume calculator.

Horizontal cylindrical tanks are not linear. Lying on its side, the liquid forms a circular segment whose area grows slowly near the bottom, fastest at the middle, and slowly again near the top. Below the halfway point you calculate the filled segment directly; above it you calculate the empty segment at the top and subtract it from the total. The horizontal cylindrical tank volume calculator does this tank-volume-by-liquid-depth math for you.

Capsule, oval, cone, conical, and spherical tanks also have nonlinear fill behaviour, because their cross-section changes with height. A spherical tank, for example, fills as a spherical cap rather than in proportion to depth. In every case the site calculator handles the partial-fill math automatically, so you only need the liquid level and the tank's dimensions. To turn that depth-to-volume relationship into a full printable table, the tank dip chart generator lists the volume at every level from empty to full.

When measuring, use inside dimensions where possible, take the radius as the diameter ÷ 2, and treat fill height as the liquid depth from the bottom of the tank. Real capacity can still differ from the calculated figure because of wall thickness, fittings, tilt, baffles, and manufacturing tolerances.

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. Run the numbers with the vertical cylindrical tank volume calculator.

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. The horizontal cylindrical tank volume calculator does this at any liquid depth.

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. Try the rectangular tank volume calculator.

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. The capsule tank volume calculator covers both horizontal and vertical capsules.

Oval (stadium) and elliptical tanks

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. A true elliptical tank instead has a genuine ellipse cross-section, with volume V = (π × width × height × L) / 4 — different from a cylindrical tank fitted with 2:1 elliptical or dished heads. The oval tank volume calculator handles both the stadium oval and the true ellipse on one page.

Cone, conical 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 — see the conical tank volume calculator for cones and inverted cones. 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.

Spherical tank

A spherical tank holds the volume of a full sphere, V = (4/3) × π × r³. Partial fill is a spherical cap of liquid height h, V = (π × h² / 3) × (3r − h), so it does not fill in proportion to depth. The spherical tank volume calculator works it out with a worked example.

Converting to gallons and litres

Once you have a volume in cubic units, convert it with these standard factors:

The key is to keep your units consistent and not mix them in one calculation. Measure in inches and work in cubic inches; measure in feet and work in cubic feet; for metric, use metres and cubic metres, or centimetres and 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.

Frequently asked questions

What is the easiest way to calculate tank volume?

Find the area of the tank's cross-section and multiply by the length or height, then convert to gallons or litres. The simplest route is to enter your dimensions into the tank volume calculator, which applies the right formula for each shape automatically.

How do I calculate the volume of a partially full tank?

Use the liquid level (fill height) instead of the full height. For rectangular and vertical cylindrical tanks the volume rises in direct proportion to liquid depth; for horizontal cylinders, capsules, cones, and spheres the fill is nonlinear and needs the shape's segment or cap formula.

Why is a horizontal cylindrical tank harder to calculate when partially full?

Because the liquid forms a circular segment whose area changes nonlinearly with depth. You compute the segment area at the liquid level (and, above the halfway point, subtract the empty segment from the total), then multiply by the tank length — which is why a calculator is easier than doing it by hand.

How do I convert tank volume to gallons?

Divide cubic inches by 231, or multiply cubic feet by about 7.48052, to get US gallons. One US gallon also equals 3.785411784 litres.

How do I calculate tank volume in litres?

Convert the volume to cubic metres and multiply by 1,000 (1 cubic metre = 1,000 litres), or multiply US gallons by 3.785411784. Keep every measurement in the same unit system before converting.

Should I use inside or outside tank dimensions?

Use inside (internal) dimensions where you can, since wall thickness, fittings, and baffles reduce the usable space. Outside dimensions overstate the capacity slightly.

Which calculator should I use for my tank shape?

Match the shape: vertical or horizontal cylindrical, rectangular, capsule, oval/elliptical, cone/conical, cone-bottom/cone-top, or spherical. Each has its own calculator, and the main tank volume calculator covers all supported shapes including partial fill.

Try it yourself

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

Related tank guides

For practical real-world tank questions beyond volume calculation, see these reference guides:

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.