Tank Volume & Fill Level Calculator

About this calculator

A tank’s capacity is the easy half of the question. The half that actually costs money is the other one: how much is in it right now, given a dipstick reading. For an upright cylinder or a rectangular sump those are the same question — half the depth is half the volume. For a cylinder lying on its side, a capsule, a cone-bottom hopper or a vessel with dished heads, they are not: a horizontal drum filled to a quarter of its diameter is 19.55% full, not 25%. This calculator covers nine tank geometries, gives you both figures at once, and prints a dipstick table at 10% depth increments so you can take the answer to the tank with you.

How to read your results

The headline figure is the volume at the fill depth you have set, and its caption changes with it — it reads “Total capacity” only while the tank is full, and “Volume at this depth” the moment you move the depth slider, so a saved or shared result can never be mislabelled. The unit selector sits on that figure itself, so you can switch between litres, US gallons, imperial gallons, cubic metres and cubic feet without re-running anything — ordering, regulating and metering rarely agree on a unit. Beside it, the diagram draws your tank to the proportions of the dimensions you typed, with the liquid shaded to the depth you set and each dimension letter marked where it belongs; if the drawing looks wrong, a dimension has gone into the wrong box. Underneath sit the total capacity, the percentage full, the ullage (the headspace left above the liquid), the depth against the tank’s maximum, and the nominal mass. Open the disclosure below for the dipstick table, which tabulates depth against volume every 10% of depth, and for the assumptions this calculator makes.

How it's calculated

Every length is converted to metres on entry and every volume is computed in cubic metres; litres, gallons and cubic feet are produced only at the moment of display, so no intermediate is ever rounded. Total capacity is the standard solid volume. Partial fill uses four primitives: the circular-segment area A = R²·acos((R−h)/R) − (R−h)·√(2Rh − h²) for liquid lying in a horizontal cylinder; the spherical cap V = ⅓πh²(3R − h) for hemispherical ends; the conical frustum V = ⅓πh(R₁² + R₁R₂ + R₂²) for cone bottoms, with the liquid-surface radius interpolated linearly up the cone; and the ellipsoid cap V = (πabh²/3c²)(3c − h) for dished heads, which reduces exactly to the spherical cap when the ellipsoid is a sphere. Capsules, ovals and dished-head tanks are evaluated branch by branch — bottom head, straight shell, top head — with each branch made continuous with its neighbour at the join. Two numerical details matter more than they look: the acos and square-root arguments are clamped before evaluation, because at zero depth and at full depth binary floating point overshoots ±1 and acos returns NaN; and the two hemispherical ends of a horizontal capsule together hold exactly ONE spherical cap of the liquid depth, not two, because the two halves mate into a single sphere — doubling it overstates a full tank by 25%. Unit conversions use the NIST SP 811 Appendix B.9 factors (US gallon 3.785412 × 10⁻³ m³, imperial gallon 4.54609 × 10⁻³ m³, cubic foot 2.831685 × 10⁻² m³, litre 10⁻³ m³); the imperial gallon is independently fixed at 4.54609 cubic decimetres by the Weights and Measures Act 1985.

Worked example

A steel drum lying on its side, 2 m internal diameter and 2 m long, with the dipstick reading 0.5 m — a quarter of the way up the diameter.

The segment area is 1²·acos((1 − 0.5)/1) − (1 − 0.5)·√(2 × 1 × 0.5 − 0.5²) = 1.0472 − 0.4330 = 0.6142 m², and multiplying by the 2 m length gives 1.2284 m³ — 1,228 litres, or 324.5 US gallons. Total capacity is π × 1² × 2 = 6.2832 m³ (6,283 litres). So the drum is 19.55% full, not the 25% the dipstick reading suggests: reading the depth as a percentage would overstate the contents by nearly 350 litres.

Frequently asked questions

Why isn’t a tank half full when the liquid is halfway up?

It usually is, but only for shapes whose cross-section does not change with height — an upright cylinder, a rectangular sump, an upright oval. In those, depth and volume rise together. A cylinder lying on its side is different: the widest part of the circle is at the middle, so the first quarter of the depth holds much less than the second quarter. By symmetry it is still exactly half full at exactly half the diameter, but at every other depth the two percentages diverge, reaching about 5.5 points of difference at a quarter and three-quarters depth. Capsules, cone bottoms and dished heads behave the same way, for the same reason.

Should I measure the inside or the outside of the tank?

The inside, always. Every dimension this calculator asks for is internal, and measuring the outside with a tape overstates capacity — for a 1 m polyethylene water tank with 6 mm walls, by about 3.6%, which on a 1,000-litre tank is 36 litres you do not have. If you can only reach the outside, subtract twice the wall thickness from each width or diameter and twice again from the height. This is by far the most common reason a tank calculator appears to disagree with reality.

What is ullage?

Ullage, sometimes called outage or headspace, is the empty volume above the liquid — total capacity minus contents. It is the number you need when you are filling rather than emptying: how much more will fit. It matters practically as well as arithmetically, because most liquids need a deliberate ullage allowance for thermal expansion, and fuel tanks in particular are normally filled to around 95% rather than to the brim.

Can I use this instead of the manufacturer’s strapping chart?

For sizing, ordering and day-to-day stock checks, yes. For custody transfer — a metered sale, a tax-assessed volume, a legally weighable quantity — no. A strapping chart is produced by physically calibrating that individual vessel, so it captures the manufacturing tolerances, the weld seams, the dents and the internal fittings that a geometric formula by definition cannot. Where a strapping chart exists, it governs.

Are 2:1 elliptical heads modelled exactly?

They are modelled as ideal semi-ellipsoids of depth D/4, which is the geometric shape the “2:1” name describes. Real ASME F&D heads are torispherical — a spherical crown blended into a toroidal knuckle — and hold roughly 1–2% less than the ideal ellipsoid. If your vessel’s drawing states a head volume, trust the drawing. If your heads are not 2:1, the head depth field is editable.

What about a tank installed on a slope?

Sloped installation is out of scope, and this is a real limitation rather than an oversight: buried fuel tanks are routinely set with a deliberate fall towards one end so that water and sediment collect where they can be pumped out. A tilt changes the depth-to-volume relationship in a way that depends on the tilt angle and on which end you dip, so a level-tank chart applied to a tilted tank will be wrong at every reading except the full and empty ones.

Why do US and imperial gallons give such different answers?

Because they are genuinely different units of the same name. A US gallon is 3.785412 litres and an imperial gallon is 4.54609 litres — the imperial one is about 20% larger. The imperial gallon is fixed in UK statute at 4.54609 cubic decimetres; both figures here come from the NIST conversion tables. If a tank’s stated capacity looks about a fifth off, this is almost always why.

Sources

• mathworld.wolfram.com/HorizontalCylindricalSegment.html — Wolfram MathWorld
• mathworld.wolfram.com/SphericalCap.html — Wolfram MathWorld
• mathworld.wolfram.com/ConicalFrustum.html — Wolfram MathWorld
• www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9 — National Institute of Standards and Technology
• www.legislation.gov.uk/ukpga/1985/72/schedule/1 — The National Archives

Reviewed by the YouCalc Team · Last reviewed May 24, 2026