Tank Volume Calculator
Pick your tank's orientation and head shape, enter its dimensions, and get total capacity plus fill volume instantly.
Worked examples
LPG storage vessel dipped to 1 m
A site technician checks how much propane is in a horizontal pressure vessel with standard 2:1 elliptical heads by reading the dipstick.
- D
- 2 m
- L
- 4 m
- h
- 1 m
≈ 7,330.4 L filled, of 14,660.8 L total capacity
Feed hopper tapering to a narrower outlet
A plant operator sizes a vertical mixing hopper that tapers from a 2 m base to a 1 m outlet, filled 2 m up its 3 m height.
- D-bottom
- 2 m
- D-top
- 1 m
- H / h
- 3 m / 2 m
≈ 4,421.5 L filled, of 5,497.8 L total capacity
Checking a flat-bottomed water tank partway through filling
A facilities tech wants to know how much water is already in a plain vertical tank before deciding when to stop the fill pump.
- D
- 3 m
- H
- 4 m
- h
- 2.5 m
≈ 17,671.5 L filled, of 28,274.3 L total capacity
Cross-checking a rectangular dosing sump
Rectangular tanks and sumps aren't one of the shapes above — their volume is a plain length × width × depth multiplication, worth doing by hand before trusting a vendor cut sheet.
- L
- 1.2 m
- W
- 1.0 m
- h
- 0.8 m
1.2 × 1.0 × 0.8 = 0.96 m³ = 960.0 L (253.6 gal)
How the formula works
Every horizontal shape here starts from the same picture: slice the tank's straight cylindrical shell at a right angle and you get a circle of radius r; liquid filled to height h cuts off a circular segment — the area below a horizontal chord. That chord sits a perpendicular distance r − h from the center, so the half-angle to its endpoints is acos((r−h)/r), and the segment's area follows directly from the full central angle θ. Multiply by the shell's length L and you have the wetted volume of the straight section.
Domed heads extend this the same way for every head style: a hemispherical, 2:1 elliptical, or custom head is just a sphere stretched (or compressed) along its axis by a depth-to-radius ratio a/R. That affine stretch scales the classic spherical-cap volume formula directly, which is why a sphere, a hemisphere-headed tank, and a 2:1-headed tank all resolve to one capped-ellipsoid formula with a as the only shape parameter — a=R gives a hemisphere, a=R/2 gives the 2:1 standard, and a=0 collapses it to a flat head worth zero volume. Vertical cone/frustum tanks use a different but equally direct idea: the radius tapers in a straight line from bottom to top, so stacking circular disks of that changing radius up to height h and integrating gives a closed-form cubic — no iteration needed. An oval (elliptical) cross-section is simply this same segment math with the circle stretched into an ellipse, scaling one axis by W/H.
The segment formula is also the precise answer to "why isn't half the depth half the tank." Take a plain 2 m diameter horizontal shell (r=1 m) with no heads. Filled to a quarter of its diameter (0.5 m) the wetted cross-section is only 19.6% of the full circle, not 25% — the tank is at its narrowest right there. Filled to three-quarters of its diameter (1.5 m) the wetted area is already 80.4%, not 75%, because by then the widest part of the circle is fully submerged and only the narrow crown stays dry. Those two numbers aren't independent: 19.6 and 80.4 sum to exactly 100, because a circle — and, with heads fitted, the capped-ellipsoid head volume too — is point-symmetric about its centre. That makes the halfway depth the one point where "half the depth is half the tank" is exactly true on any horizontal tank, whatever its diameter or head shape. Move away from that midpoint and the gap between the naive guess and the real answer grows fastest first, then narrows again near the ends: on this same 2 m shell the worst-case gap is nearly 6 percentage points, around 19% and 81% of full depth — 13.2% actual against a 19% guess, and 86.8% actual against an 81% guess — not, as intuition suggests, right in the middle where the reading is actually exact.
Vertical cone/frustum tanks break that symmetry outright, because their cross-section doesn't just get eclipsed by a rising chord — it genuinely changes size with height. The feed hopper worked example above tapers from a 2 m base to a 1 m outlet over 3 m of height; filled to two-thirds of that height (2 m) it already holds 80.4% of its rated capacity, well ahead of the 66.7% depth fraction, because most of the tank's cross-sectional area sits low, near its wide base. A hopper shaped the other way — narrowing toward the outlet instead of the top — runs the bias in reverse: depth climbs for a long time near the bottom while volume barely moves, which is exactly why a low-level alarm on a cone-bottom tank needs to trigger well before the stick "looks empty."
Tank heads: how much extra volume each shape adds
The calculator's "Head depth — Distance X (a)" field is the same measurement every tank fabricator's drawing calls the head's dish depth, or crown height — how far the end bulges out past the point where it stops being a straight cylindrical shell. Three of the five horizontal-tank options on this page are just named presets for that one number: flat sets a=0 (no bulge, zero added volume), 2:1 semi-elliptical sets a=D/4 — literally what "2:1" means, a head whose overall width is twice its depth — and hemispherical sets a=R, a full radius of bulge. "Custom ellipsoidal heads" leaves a as a free input for anything in between, or beyond, those three presets.
Torispherical heads — often stamped "dished" or "F&D" (flanged and dished) on a nameplate, and the most common head on lower-cost horizontal propane, NH₃, and chemical-storage vessels — aren't a stretched ellipse at all. They're a genuinely different, compound shape: a spherical crown blended into the straight shell through a toroidal knuckle of a smaller radius, standardized in the ASME Boiler and Pressure Vessel Code, Section VIII, Division 1 (UG-32(e)) as a crown radius equal to the vessel's diameter with a knuckle radius of 6% of that diameter. Working through that geometry gives a dish depth of about 0.169×D — noticeably shallower than a true 2:1 ellipse's 0.25×D on the same diameter, which is why a torispherical head holds roughly two-thirds as much volume as a 2:1 elliptical head of the same size (0.169 ÷ 0.25 ≈ 0.68, and because the capped-ellipsoid formula above is linear in a, that ratio carries straight through to volume). Since this calculator doesn't model the compound torispherical shape directly, "Custom ellipsoidal heads" with a measured (or 0.169×D-estimated) dish depth is the practical stand-in — it runs a percent or two high on the head's own volume, because a smooth ellipse sweeps out slightly more than a knuckled torisphere of the same depth, but that's a rounding error against the tank's total capacity, not a reason to avoid the approximation.
Which shape to expect also tracks which code the tank was built to. Field-erected, atmospheric-pressure storage tanks — the large flat-bottomed cylinders API 650 governs — are almost always flat-headed for volume purposes, with a cone or dome roof that sits above the normal liquid level and contributes nothing to capacity. Shop-built pressure vessels — propane bullets, compressed-air receivers, process reactors — fall under ASME BPVC Section VIII and use one of the three domed shapes above, chosen for the pressure rating and fabrication cost the application calls for.
| Head shape | Depth ratio (a) | Added volume | Share of total capacity |
|---|---|---|---|
| Flat (straight) | a = 0 | 0.0 L | 0% |
| Torispherical (ASME F&D, "dished") | a ≈ 0.169 × D | 1,415.8 L | ≈10.1% |
| 2:1 semi-elliptical | a = D/4 | 2,094.4 L | ≈14.3% |
| Hemispherical | a = R (= D/2) | 4,188.8 L | ≈25.0% |
Sources: the flat, 2:1 elliptical, and hemispherical depth ratios follow directly from the capped-ellipsoid derivation above (a=0, D/4, and R respectively). The torispherical ("flanged and dished") proportions — crown radius equal to the shell diameter, 6% knuckle radius — and the resulting ≈0.169×D dish depth reference ASME BPVC Section VIII Division 1, UG-32(e), cross-checked against published pressure-vessel design references (Chemical Engineering magazine's pressure-vessel design guide; Pressure Vessel Engineering's head-type comparison). Flat-bottomed atmospheric storage tank practice: API 650.
What this calculator can't see: slope, wall thickness, expansion, and dead stock
This page assumes the tank sits level and true — enter a diameter and a length and it treats the shell as a perfect, unslanted cylinder. Real horizontal tanks are very often installed with an intentional slope toward the outlet, so the last bit of product can actually reach the pump, and vertical tanks settle unevenly on their foundation over the years. A one- or two-degree tilt barely moves the reading near half-full, but it visibly shifts the answer near empty or near full — exactly where the liquid surface sits closest to the low or high end of the shell. Handling a known tilt properly means working the geometry per-depth rather than as one single calculation; see how a strapping chart accounts for it in building a strapping chart by hand.
Every diameter this calculator asks for is the tank's inside diameter (ID) — the dimension liquid actually occupies — not the outside diameter (OD) a tape reads wrapped around the shell, and not a nominal or nameplate size a manufacturer rounds for ordering convenience. On a thin poly tote or a light-gauge drum, ID and OD are close enough to ignore. On a thick steel pressure vessel, a heavy fiberglass tank, or anything with insulation cladding, wall thickness alone can shift the diameter by a percent or more — and because a cylinder's volume scales with the square of the radius, that error doubles by the time it reaches the final number. Building a strapping chart by hand works through the exact inside-diameter = (C÷π) − 2t conversion for going from an outside strap measurement to the figure this calculator actually wants.
A tank's own shell barely moves with temperature — steel and fiberglass expand little enough to ignore for capacity work. The liquid inside is a different story: warm it and it genuinely occupies more space, so the same mass of product reads a larger volume hot than cold. Petroleum measurement handles this formally through API MPMS Chapter 11.1, which publishes volume correction factor (VCF) tables referenced to 60°F (15.56°C) so a delivery ticket, a tank gauge, and a meter reading all agree regardless of what temperature each one happened to be taken at. For how large that effect actually gets and when it's worth correcting for outside a custody-transfer context, see why density tables say 20°C (and when to correct).
Every real tank also has some liquid the outlet can never draw — sediment settled below a suction line's mouth, a low sump the pump isn't plumbed into, the last centimetre a floating suction never quite reaches. This calculator, like the geometry underneath it, measures fill height from the lowest point the shell itself defines; it has no way to know where the physical outlet actually sits inside that shell. That's a deliberate scope choice, not an oversight, but it means "total capacity" from this page and "usable volume" on an operations spec sheet are two different numbers on purpose — worth measuring once per tank rather than assumed to be zero.
From one answer to a full chart: connecting this to a real gauge reading
This page answers one question at a time: at this dimension and this fill height, what's the volume? A dip chart or strapping table answers that same question at every depth at once, which is what actually belongs taped to the side of a tank someone reads with a stick. The tank strapping chart calculator runs the exact same shell-plus-heads geometry as this page but sweeps it across the full depth range and prints every row, so the two tools share their formulas rather than risk disagreeing with each other.
Once a chart exists — printed, generated, or read off a nameplate — using it correctly has its own failure modes, and most of them have nothing to do with geometry: confusing an innage reading with an ullage reading, dipping right at the unforgiving middle of a horizontal tank instead of averaging a few readings, or trusting an old chart's tilt assumption on a tank that's since settled. Reading a tank dip chart without fooling yourself works through those specifically. If there's no chart at all — a tank inherited with no paperwork, or one welded up in a yard with no drawing — building a strapping chart by hand covers taking the measurements yourself, tape and all, including the wall-thickness correction mentioned above. And for the simplest possible case — a plain straight cylinder, no heads, nothing tapered — the cylinder volume calculator runs just that one shape end to end.
Frequently asked questions
I don't know my tank's head shape — which option should I pick?
Check the tank's spec plate or purchase drawing first — pressure vessels almost always state the head type ("2:1 elliptical," "hemispherical," or "flat"). If you're measuring by hand, compare the head's bulge depth to its radius: a bulge of about a quarter of the radius is a 2:1 elliptical head (the ASME default for most process tanks), a bulge equal to the full radius is a hemispherical head (common on propane and pressure tanks), and a nearly flat end is a flat head (typical of basic cylindrical drums and IBCs). If it's somewhere in between, use "Custom ellipsoidal heads" and enter the measured bulge depth directly.
What's the difference between total capacity and filled volume?
Total capacity is how much the tank holds completely full, based only on its shape and dimensions — it's always calculated. Filled volume is how much liquid is inside right now, based on the fill height you measured. Leave the fill height field blank if you only want the tank's rated capacity; fill it in to also see the current volume and the fill percentage.
Why doesn't the diagram show the width (W) I entered for an oval tank?
The width of an elliptical cross-section is the tank's depth going into the page from this side view — the same reason you can't see a hallway's width by looking at it from one end. The diagram shows the two dimensions that define the profile you'd actually see standing beside the tank (length and cross-section height); width only becomes visible from an end-on view, which is why it still needs its own input even though the picture doesn't draw it.
How is a cone-bottom (frustum) tank different from a straight cylinder?
A frustum tapers linearly between two different diameters — a bottom diameter and a top diameter — over its height, so its cross-sectional area at the liquid surface changes with fill level even though the shape isn't curved. Set the top diameter to zero for a tank that comes to a sharp point (a true cone), or set it equal to the bottom diameter to get a plain straight-sided cylinder — the same taper formula reduces exactly to a regular cylinder's volume in that case, so there's no need to switch shapes.
Where should I measure the fill height from?
Always from the lowest interior point the liquid can reach, straight up to the liquid surface — for a horizontal tank that's the bottom of the round shell itself, not the top of the support saddles or legs it's resting on. For a cone-bottom or sphere-bottom vertical tank, that lowest point is the tip of the cone or the bottom of the sphere, not the top of any flat base plate underneath it.
My result differs slightly from another tank calculator online — why?
It's almost always a unit-conversion rounding difference, not a formula error. Some older tools use conversion factors rounded to 4-5 significant figures internally (for example, converting cubic feet to gallons at 7.4805 instead of the exact 7.480519...), which compounds into a few parts-per-million of drift on the final number. This calculator uses the exact NIST-defined conversion constants throughout, so if you need to match a legacy tool's output exactly, expect agreement to about 4 significant figures rather than every decimal place.
My tank has dished (torispherical) ends — should I pick 2:1 elliptical or Custom?
Pick Custom ellipsoidal heads and enter the head's measured dish depth. A torispherical or "F&D" head is a genuinely different shape from a 2:1 ellipse — a spherical crown blended into the shell through a separate, tighter knuckle radius — and it's shallower for the same diameter (roughly 0.169×D deep for the ASME-standard 6% knuckle, versus a 2:1 head's 0.25×D), so treating a dished head as a 2:1 head will overstate its volume noticeably. Entering the actual measured depth into Custom gets you within a percent or two of the true torispherical volume, which is as close as a single depth parameter can get without modeling the compound crown-and-knuckle shape directly.
Should I enter the tank's inside diameter or outside diameter?
Inside diameter (ID) — the dimension the liquid actually occupies. A tape wrapped around the shell measures the outside diameter (OD), and a nameplate or purchase spec often lists a nominal size rounded for ordering, so neither is quite what the formula wants. On a thin poly tote the ID/OD gap is negligible; on a thick steel pressure vessel or an insulated, clad tank it can run a percent or more, and because volume scales with diameter squared, that error roughly doubles by the time it reaches the answer. If you only have an outside strap measurement, subtract twice the wall (and cladding) thickness before entering it — see the worked conversion in the guide on building a strapping chart by hand.
The number I calculated doesn't match the capacity stamped on the tank's nameplate — why?
A handful of real-world gaps commonly explain a few percent of difference, and none of them means the formula is wrong. The nameplate figure may already exclude dead stock (liquid below the outlet the pump can never draw), may be rounded down deliberately as a safety margin, may assume the exact inside dimensions from a fabrication drawing rather than a field tape measurement, or — on an installed tank — may not account for a slight tilt that's crept in since it was leveled. None of these are geometry errors; they're the difference between a tank's theoretical full-shell capacity, which is what this calculator reports, and its certified or practical working capacity, which a nameplate is trying to state more conservatively.