Tank Volume Calculator
Calculate Smarter. Work Faster.
Total and filled capacity for 10 tank shapes — cylinders, rectangles, ovals, capsules, 2:1 elliptical and dished heads — in US gallons, liters, m³, ft³, quarts and imperial gallons.
Tank Type & Dimensions
Applies to every dimension field below, including Filled Depth.
Measured vertically from the bottom of the tank. Leave blank to see total capacity only.
Horizontal Cylinder
Illustrative diagram showing the dimensions each field refers to. The liquid level shown is a fixed example and does not track the Filled Depth you enter.
| Unit | Total Capacity | Filled Volume |
|---|---|---|
| US Gallons | — | — |
| US Quarts | — | — |
| Imperial Gallons | — | — |
| Liters | — | — |
| Cubic Meters | — | — |
| Cubic Feet | — | — |
Calculations assume inside dimensions and an idealized geometric model of the selected shape; Horizontal Dish Ends uses a standard flanged-and-dished (F&D) approximation rather than exact torispherical geometry. Actual tanks may have wall curvature, fittings, or heads that differ slightly from these idealized shapes — treat results as estimates for planning and inventory purposes.
Tank volume calculations, explained
Every shape here reduces to the same basic idea: find the cross-sectional area at each point along the tank, and integrate it along the tank's length or height. For the five shapes with uniform, flat-ended cross-sections — Horizontal Cylinder, Vertical Cylinder, Rectangle, Horizontal Oval, and Horizontal Ellipse — that cross-section never changes shape along the axis, so total volume is simply cross-sectional area × length (or height, for vertical tanks), and filled volume just needs the area of that same cross-section up to the liquid line.
Vertical Oval is a special case worth calling out separately: it's a stadium shape standing on end (rounded top and bottom, flat sides), so the liquid level cuts through curved caps rather than a constant cross-section. It uses the same three-zone method as the domed-end shapes below (bottom cap, straight middle, top cap) — just with a 2D circular segment for each curved cap instead of a 3D spherical or ellipsoidal cap.
The remaining four shapes — Horizontal Capsule, Vertical Capsule, Horizontal 2:1 Elliptical, and Horizontal Dish Ends — add curved 3D end caps to a cylindrical middle section. Their total volume is the cylinder's volume plus the volume of the two end caps combined. For filled volume, this calculator uses a standard trick from horizontal-tank strapping charts: two identical opposite end caps, sliced at the same liquid height, together hold exactly as much liquid as a single combined solid of that cap shape (two hemispheres make one full sphere; two 2:1 elliptical heads make one oblate spheroid) sliced at that same height. Dish Ends heads use the same idea, applied through numerical integration since a torispherical shape has no simple closed-form slice formula.
Cylinder: V = (π/4)·d²·l Capsule: V = (π/4)·d²·a + (4/3)π·(d/2)³
The three domed-end shapes only differ in how deep the end caps bulge relative to the diameter: a capsule's ends are full hemispheres (depth = d/2), a 2:1 elliptical head is shallower (depth = d/4), and a dished (F&D) head is shallower again (depth ≈ 0.169×d for standard proportions). Deeper heads add proportionally more volume for the same overall tank length — useful to know when comparing a capsule-shaped propane tank to a flat-headed rectangular tote of similar footprint.
Worked Example — Horizontal Capsule
A horizontal capsule tank has a 1.2 m diameter and a 2.5 m straight cylindrical section, filled to a depth of 0.8 m.
- Total capacity = (π/4)×1.2²×2.5 + (4/3)π×0.6³ = 2.827 + 0.905 = 3.732 m³ ≈ 3,732 L ≈ 986 US gal
- Filled volume at 0.8 m depth: circular-segment area at 0.8 m (of the 1.2 m circle) × 2.5 m, plus the equivalent spherical-cap volume at 0.8 m of a 1.2 m sphere
- Filled volume ≈ 2,673 L ≈ 71.6% of total capacity, even though the liquid depth (0.8 m) is only 67% of the diameter — because the cross-sectional area available to hold liquid grows non-linearly as the level rises toward the centreline
This non-linear relationship between depth and filled percentage is exactly why a dipstick chart for a horizontal tank is never a straight line — use the Filled Depth field above to check any level directly instead of estimating by eye.
All results assume the tank is level, the geometry is an idealized solid (no internal baffles, fittings, or wall curvature irregularities), and dimensions entered are internal (inside) measurements.
Matching your tank to the right shape and head type
If you're not sure which of the 10 shapes matches your tank, this quick reference covers the most common real-world tanks and which option to pick:
| Common tank | Pick this shape |
|---|---|
| Propane / LPG bullet tank, small air receiver | Horizontal Capsule |
| Vertical LPG bullet, small vertical air receiver | Vertical Capsule |
| Large ASME pressure vessel with semi-elliptical heads | Horizontal 2:1 Elliptical |
| Low-pressure storage tank with flanged & dished (F&D) heads | Horizontal Dish Ends |
| Fuel/water tank welded from flat plate, rounded corners, flat ends | Horizontal or Vertical Oval |
| Open-top water tank, silo, drum standing upright | Vertical Cylinder |
| Rectangular tote, sump, or concrete tank | Rectangle |
| Flat-ended tank with a true elliptical (not stadium) cross-section | Horizontal Ellipse |
When in doubt between a capsule and an oval, look at the tank's ends from the side: if the ends themselves bulge outward in a dome (you'd see curvature looking straight at the flat end), it's a capsule-family shape (Capsule, 2:1 Elliptical, or Dish Ends). If the ends are flat plates and only the tank's cross-section (viewed from either end) is rounded on the sides, it's an Oval or Ellipse.
Why a dipstick reading misleads you on a horizontal tank
Assuming that liquid depth percentage equals volume percentage is a common source of tank inventory errors in day-to-day plant operation, and it catches experienced people out. On a vertical tank, the arithmetic is forgiving: the cross-section never changes, so half the depth really is half the volume, and a stick marked in equal increments gives equal volume steps all the way up. On a horizontal cylindrical tank, none of that holds. The tank is widest across its middle and pinches to nothing at the top and bottom, so equal steps of depth are not equal steps of volume.
The practical result: if someone reads the stick, sees the liquid at a quarter of the tank's diameter, and reports the tank as "about 25% full," the number is wrong — and it is wrong in a predictable direction. Below the halfway mark a straight-line guess always over-states the contents; above the halfway mark it always under-states them. The only depth where the naive estimate is exactly right is dead centre.
Depth percentage vs actual volume percentage
These figures are for a plain horizontal cylinder (flat ends). They depend only on the ratio of liquid depth to tank diameter, so the same table applies to any horizontal cylindrical tank regardless of its size or length:
| Liquid depth (% of diameter) | Actual volume (% of capacity) | Error if you assume they match |
|---|---|---|
| 10% | 5.2% | Over-reads by 4.8 points |
| 20% | 14.2% | Over-reads by 5.8 points (worst case) |
| 25% | 19.6% | Over-reads by 5.4 points |
| 40% | 37.4% | Over-reads by 2.6 points |
| 50% | 50.0% | Exact — the only point that matches |
| 60% | 62.6% | Under-reads by 2.6 points |
| 75% | 80.4% | Under-reads by 5.4 points |
| 80% | 85.8% | Under-reads by 5.8 points (worst case) |
| 90% | 94.8% | Under-reads by 4.8 points |
Values computed from the circular-segment area of a horizontal cylinder; the pattern is symmetrical about the 50% point.
What that costs on a real tank
Take a common size of horizontal storage tank: 8 ft diameter by 27 ft long, roughly 10,150 US gallons (about 38,400 litres) when full.
- Liquid at quarter depth (24 in on the stick): actual contents about 1,985 gallons, not the 2,538 gallons a "quarter full" assumption gives — a 553 gallon gap.
- Liquid at three-quarter depth (72 in): actual contents about 8,168 gallons, not 7,614 — the same 553 gallons, now in the opposite direction.
On a single tank that is a delivery-sized error. Across a tank farm, reconciled monthly, it is the kind of discrepancy that gets blamed on leaks, theft, or meter drift long before anyone questions the gauging method.
Where reading precision matters most
There is a second, less obvious consequence. Because the tank is widest at its centreline, each inch of depth is worth far more volume in the middle of the tank than near the top or bottom. On that same 8 ft × 27 ft tank:
- Near the middle (around 48 in depth): roughly 135 gallons per inch.
- Near the top or bottom (around 6 in or 90 in): roughly 65 gallons per inch — less than half as sensitive.
So a stick misread by one inch costs you about twice as much accuracy when the tank is around half full as it does when it is nearly empty or nearly full. If you are gauging a tank in the mid-band, that is where careful reading, a clean stick, and a properly fixed dip point actually pay off. It also means an operator who "rounds to the nearest inch" is introducing a much larger error at mid-level than the same habit would cause on a vertical tank.
End caps make it worse again
Everything above assumes a plain cylinder with flat ends. Most real pressure vessels and bulk tanks have domed heads — hemispherical, 2:1 semi-elliptical, or flanged-and-dished. Those heads hold extra liquid that the simple circular-segment calculation does not account for, and they contribute it in their own non-linear way as the level rises. Pick the shape that actually matches your vessel in the calculator above rather than defaulting to Horizontal Cylinder, or you will understate the contents — most noticeably on short, large-diameter tanks where the heads are a large fraction of the total volume.
How tanks are actually calibrated in the field
A geometric calculation like the one on this page tells you what an ideal tank of those dimensions would hold. For custody transfer, regulatory reporting, or any figure that has money attached to it, that is not the number the industry works from. Instead, each tank gets its own tank table (also called a capacity table, gauge table, or strapping table) — a calibrated lookup of gauge height against volume, produced for that specific vessel and periodically revalidated. Understanding how that table is built explains most of the gaps between a clean calculation and what the tank really holds.
The two main calibration methods
Manual strapping (geometric). The tank's external circumference is measured with a calibrated tape at several heights, because a real shell is never perfectly uniform — plate courses differ, welds add thickness, and older tanks bulge. Those measurements are then corrected inward to get internal dimensions: plate thickness and any insulation, lining, or coating is subtracted. The result is a course-by-course model of the tank rather than a single nominal diameter. This is the closest relative to what this calculator does, but with the real measured shell instead of a drawing figure.
Liquid calibration (volumetric). Known volumes of liquid are metered into the tank and the level is recorded at each step, building the table directly from measurement. It is slower and needs a calibrated meter or prover, but it gives a direct measurement-based representation of the vessel's actual capacity — which matters most for tanks that geometry struggles with: vessels with heavy internal furniture, irregular or repaired shells, or unusual shapes. Where the two methods disagree on an in-service tank, the liquid calibration generally reflects the tank as it now stands.
Deadwood — the correction people forget
"Deadwood" is the trade term for anything inside the tank that displaces liquid or adds space, and it is the most commonly missed correction when someone sizes a tank from a drawing. It cuts both ways:
- Subtracts volume: internal heating or cooling coils, agitator shafts and impellers, baffles, internal supports and stiffeners, ladders, standpipes, mixers, submerged pumps.
- Adds volume: sumps and drain-down wells below the main shell, large nozzle bores, manway barrels, and any dished bottom section below the datum.
On a clean, empty storage tank the correction may be negligible. On a jacketed and agitated process vessel it can be a significant fraction of the nominal capacity — which is why a process vessel's working volume is often noticeably less than its geometric volume, and why the two figures should never be used interchangeably in a mass balance.
Out-of-level and tilt
Horizontal tanks are unusually sensitive to this, and it is worth checking before blaming the maths. Many horizontal tanks are deliberately installed with a slight fall toward a drain or sump so they can be emptied and so water drops out at one end. That tilt means the liquid surface is no longer parallel to the tank axis, so the depth at the dip point is not the average depth along the tank, and the level-to-volume relationship shifts — most noticeably when the tank is nearly empty, where the liquid is pooled at one end and a stick at the other end may read essentially nothing while there is still usable product inside. Settlement of foundations or saddles over the years produces the same effect without anyone having designed it in. Vertical tanks are affected too, but the error is generally smaller for the same amount of tilt.
Fix the dip point and the datum
A tank table is only meaningful against a defined reference. The dip point must be a fixed, marked location with a datum plate beneath it, and everyone gauging that tank must use the same one. Gauging from a different nozzle, or from a hatch that happens to be more convenient that shift, quietly invalidates the table — the reference height changes, so every reading is offset by a constant that nobody has written down. Where a tank has been re-roofed, had nozzles moved, or been repaired, the datum should be re-established rather than assumed.
Temperature: the liquid and the steel both move
Two separate effects get confused here. The liquid expands and contracts with temperature, so a volume measured at tank temperature is converted to a standard reference temperature — 60 °F in US practice, 15 °C in most international practice — before it is reported or invoiced. That is the larger effect for most products, and for petroleum it is handled by published volume correction factors rather than a rule of thumb. Separately, the tank shell itself expands, which slightly changes the tank's own capacity at a given gauge height; calibration standards handle this with a shell temperature correction. For a rough operational stock check neither matters much, but for anything reconciled against a meter or invoiced, both belong in the calculation.
When to recalibrate
Tank tables are not permanent. A tank should be recalibrated after any repair or modification that touches the shell, after significant settlement, after a change in internal fittings, and at whatever interval the applicable standard or the local weights-and-measures authority requires. A table produced before an agitator was installed will overstate the capacity from the day that agitator went in.
So where does this calculator fit?
It is the right tool for design and planning work: sizing a new vessel, checking whether a tank will fit a duty, estimating a bund or secondary containment requirement, sanity-checking a supplier's quoted capacity, or working out roughly how much product a partly full tank is holding. It is not a substitute for a calibrated tank table on a vessel where the number carries commercial or regulatory weight. If your calculated figure and the tank's own table differ noticeably, the table is not necessarily wrong — deadwood, shell deformation, tilt, and the difference between nominal and measured dimensions all live in that gap.
Tank calibration and static measurement practice are covered by published standards from bodies including API (in its Manual of Petroleum Measurement Standards) and ISO, with separate documents for vertical and horizontal cylindrical tanks and for the calibration methods themselves. Requirements, applicable editions, and legal metrology obligations vary by country and by what the tank is used for — confirm the specific standard and revision that applies in your jurisdiction before relying on it for custody transfer or regulatory work.
Common mistakes when calculating tank volume
1. Using outside dimensions instead of inside dimensions. Tank capacity is based on the internal volume — using the outer diameter or outer dimensions (without subtracting wall thickness) overstates capacity, more noticeably on thick-walled pressure vessels.
2. Picking Capsule when the tank actually has flat ends. A stadium-shaped (oval) cross-section with flat plate ends is a completely different shape from a round tube with domed hemispherical ends — mixing these up gives a meaningfully wrong volume, especially for shorter tanks where the end-cap volume is a larger share of the total.
3. Assuming filled percentage matches depth percentage. For any horizontal round-cross-section tank, a liquid depth at 50% of the diameter is exactly 50% full, but any other depth is not proportional — 60% depth holds noticeably more than 60% of the volume, since the tank is widest at the middle. Always use the actual filled-volume calculation, not a straight-line estimate from the dipstick reading.
4. Mixing up which dimension is the straight length for domed-end tanks. For Capsule, 2:1 Elliptical, and Dish Ends shapes, the "Straight Length (a)" field is only the cylindrical middle section — it does not include the two end-cap bulges. The tank's true overall length is longer than "a" by the combined depth of both end caps.
5. Treating a Dish Ends result as exact for fabrication purposes. The Dish Ends calculation here uses a standard approximate depth ratio for typical F&D proportions — real torispherical heads vary slightly by crown and knuckle radius, so treat the result as a close planning estimate, not a certified fabrication figure.
6. Forgetting the oval/ellipse width-vs-height relationship. For Horizontal Oval, Width must be greater than or equal to Height; for Vertical Oval, Height must be greater than or equal to Width — the rounded ends can only be as wide as the cross-section itself. The calculator flags this automatically, but it's a common data-entry mix-up when copying dimensions from a drawing.
Frequently Asked Questions
Straight answers on tank shapes, fill depth, units, and head-type accuracy.
What tank shapes does this calculator support?
Ten shapes: Horizontal and Vertical Cylinder, Rectangle, Horizontal and Vertical Oval, Horizontal and Vertical Capsule, Horizontal 2:1 Elliptical, Horizontal Dish Ends, and Horizontal Ellipse. Each uses its own geometric calculation for total capacity and, optionally, the volume at a given filled depth. The Horizontal Dish Ends result uses a standard flanged-and-dished (F&D) approximation rather than exact torispherical geometry.
How is filled volume calculated for a partially full tank?
For shapes with a constant cross-section along the tank length (Horizontal Cylinder, Rectangle, Horizontal Oval, Horizontal Ellipse) the filled volume is the cross-sectional area below the liquid level, multiplied by the tank's length. For domed-end shapes (capsule, 2:1 elliptical, dish ends) the two end caps are combined into an equivalent single solid (a sphere, an oblate spheroid, or a shallow spherical segment respectively) and sliced at the same liquid height — a standard method used for horizontal tank strapping charts.
What's the difference between a capsule, a 2:1 elliptical head, and a dished (F&D) head tank?
They differ only in how deep the rounded ends bulge relative to the tank diameter (D). A capsule has fully hemispherical ends (depth = D/2). A 2:1 semi-elliptical head is shallower (depth = D/4), the standard ASME ellipsoidal head ratio. A dished (flanged and dished, F&D) end is shallower still (depth ≈ 0.169×D for the common crown radius = D, knuckle radius = 0.06×D proportions) and blends into the shell through a small toroidal knuckle rather than a smooth curve all the way to the edge.
Are these calculations based on inside or outside dimensions?
Inside (internal) dimensions, matching how tank capacity is normally specified. If you only have outside dimensions and a known wall thickness, subtract twice the wall thickness from each diameter/width/height before entering values here.
Which units can I use for input and output?
Enter all dimensions in millimeters, centimeters, meters, inches, or feet using the unit selector — the same unit applies to every field including Filled Depth. Results are always shown in six common units at once: US gallons, US quarts, imperial gallons, liters, cubic meters, and cubic feet.
How accurate is the Horizontal Dish Ends result?
The dish-ends volume uses a standard ASME F&D approximation (crown radius = diameter, knuckle radius = 6% of diameter, giving an effective dish depth z of about 0.169×D), modeled as a shallow spherical segment rather than the full torispherical (sphere + toroidal knuckle) geometry. This is accurate to within a small percentage for standard proportions and is a common engineering approximation, but if your vessel uses a non-standard knuckle radius, treat the result as a close estimate and confirm against the actual head datasheet for fabrication or precise inventory purposes.
What if my tank has a torispherical head with a different knuckle radius than standard?
A larger knuckle radius makes the head shallower (closer to a flat plate) and a smaller knuckle radius makes it closer to a full hemisphere — the standard 6%-of-diameter knuckle used here sits at the common end of that range. If your head's actual depth is known from a datasheet, you can approximate its volume by treating it as a Horizontal Capsule (if it's close to hemispherical) or by scaling between the Dish Ends and 2:1 Elliptical results here as a bracket.
Can I use this for a partially-filled vertical tank?
Yes. Vertical Cylinder uses a simple constant cross-sectional area times liquid height, so any depth works directly. Vertical Oval and Vertical Capsule both use a three-zone method instead, since they have curved caps at the bottom and top — a circular-segment calculation for Vertical Oval's 2D rounded ends, or a spherical-cap calculation for Vertical Capsule's 3D hemispherical ends, for whichever zone the liquid level falls in.
Why doesn't my dipstick reading match the percentage full on a horizontal tank?
Because a horizontal cylinder is widest at its centreline and narrows to nothing at the top and bottom, so equal steps of depth are not equal steps of volume. Below half depth a straight-line estimate always overstates the contents and above half depth it always understates them, by as much as about 5.8 percentage points around the 20% and 80% depth marks. The only depth where a proportional guess is exactly right is 50%. Enter the measured depth in the Filled Depth field above to get the actual figure instead of estimating.
Why does my calculated volume differ from the tank's official capacity table?
A geometric calculation models an ideal tank built exactly to its nominal dimensions. A calibrated tank table is built from the real vessel and includes corrections a calculation cannot know about: deadwood (internal coils, agitators, baffles, supports that displace liquid, and sumps or large nozzles that add space), actual measured shell dimensions rather than drawing figures, shell deformation on older tanks, and any tilt or settlement. Small differences are common; a larger gap often points to significant deadwood, shell deformation, tilt, or a difference between nominal and measured dimensions.
Does a tank being slightly out of level affect the reading?
Yes, and horizontal tanks are especially sensitive. Many are installed with a deliberate fall toward a drain or sump, and foundations settle over time. When the tank is tilted the liquid surface is no longer parallel to the tank axis, so the depth at the dip point is not the average depth along the tank. The effect is most pronounced near empty, where product pools at the low end and a stick at the high end can read almost nothing while usable liquid remains in the tank.
Where on the tank is a gauging error most costly?
Around the middle. Because the tank is widest at its centreline, each unit of depth represents far more volume there than near the top or bottom — on a typical 8 ft diameter horizontal tank, roughly twice as much volume per inch at mid-level as near either extreme. A stick misread by one inch therefore costs about double the accuracy at half full compared with nearly empty or nearly full, which is where careful reading and a properly fixed dip point matter most.
Should I use this calculator for custody transfer or regulatory reporting?
No. For any figure carrying commercial or regulatory weight, use the vessel's own calibrated tank table, produced for that specific tank and revalidated at the required interval. This calculator is intended for design and planning work — sizing a new vessel, checking a tank fits a duty, estimating containment requirements, sanity-checking a quoted capacity, or gauging roughly how much a partly full tank holds. Note also that reported volumes are normally corrected to a standard reference temperature (60 °F in US practice, 15 °C in most international practice), which this calculator does not apply.
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