Why is a dipstick reading not proportional to the contents?

Because a tank on its side is not the same width all the way up. At the halfway line it is at its widest — the full diameter — and it narrows to nothing at the very top and the very bottom. So the first inch of depth covers only a narrow strip along the bottom of the tank, while an inch either side of the centreline covers the full width. The consequence is easy to state and easy to get wrong in practice: a stick reading a QUARTER of the diameter is holding about a fifth of the contents, and a stick reading a TENTH is holding about a twentieth. The error runs the wrong way for anyone watching a heating oil tank get low, because it over-reports what is left just when the remaining amount matters most. The one place the intuition works is dead centre: half the depth really is half the volume, because the top half of a circle is the mirror image of the bottom half.

How much do the ends actually matter?

On a tank whose barrel is twice its diameter, two hemispherical heads hold about a quarter of the whole capacity, and the shorter the tank the more they matter. That is more than most people expect: two hemispherical heads are not two curved caps — put together they are one complete sphere of extra capacity. The common 2:1 elliptical dished head is half as deep as a hemisphere and contributes half as much, which is still not a rounding error. Ignoring the ends does not just make the capacity figure wrong; it makes it wrong in a way that varies with fill level, because the ends are also widest at the middle. If you are working from a manufacturer's capacity figure and your own barrel-only arithmetic disagrees with it, the heads are the first place to look.

What is ullage, and why is it the number some people want?

Ullage is the empty space above the liquid — capacity minus contents. It is the figure a delivery driver works to, because what matters at the filling point is how much more will fit, not how much is already there. It is also the safety number: many liquids need headspace for thermal expansion, and a tank filled to the brim on a cold morning can vent or deform by the afternoon. Some gauges are marked in ullage rather than contents for exactly this reason, measuring down from the top rather than up from the bottom, which is a real source of confusion when two people compare readings from the same tank. If your stick is measuring down from a fill point, the number you have is ullage and this page's depth input wants the other one.

When should I stop trusting this and use the tank's own table?

Whenever the number has consequences beyond planning. This page computes an ideal cylinder, and a real tank is not one: it may be dented, slightly out of round, resting out of level in its cradle, carrying years of sludge and water in the bottom, or fitted with internal baffles that displace liquid. Any of those makes the true contents differ from the geometry, and the difference is largest near the bottom — exactly where a low-level reading is being taken. For fuel inventory reconciliation, for custody transfer, or for anything a regulator will look at, the governing figure comes from the tank's calibrated strapping table, produced by measuring that individual vessel. Use this for checking a delivery looks sane, for planning, and for understanding why the stick is behaving as it is.

Materials & Quantities

Horizontal Cylinder Tank Partial Fill Volume Calculator

How much liquid a horizontal cylindrical tank holds at a dipstick depth, with flat, dished or hemispherical ends, and the ullage left above it.

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Every formula citedNamed published standards
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Market

Imperial · sales tax

Tank diameter

The internal diameter of the cylindrical barrel.

Internal, not external — a steel tank's wall is thin enough to ignore but a plastic or bunded tank's is not, and an outer measurement on a double-skinned tank can overstate the capacity substantially. Measure at the middle rather than near a head, where a dished end has already begun to curve.

Barrel length

The straight cylindrical part, not counting the ends.

Measure the seam-to-seam length of the barrel, excluding the heads, because the heads are counted separately below. Including them here and selecting dished ends counts the same volume twice.

Liquid depth

The dipstick reading, measured from the lowest point inside the tank.

From the INSIDE bottom, which is not the same as the outside bottom of a tank sitting in a cradle or on feet. Take the reading with the tank at rest — liquid still moving reads high on one side — and remember that a tank standing even slightly out of level has a different depth at each end.

Tank ends

Flat, dished, or fully hemispherical heads.

The ends are not a rounding detail. Two hemispherical heads add a whole sphere of capacity, and on a short tank that can be a third of the total. If you are unsure, look along the tank: a flat head is a disc, a dished head bulges out in a shallow curve, and a hemisphere is obviously half a ball.

Liquid in the tank

216.5 gal

High confidence

The tank is 34% full BY DEPTH and 30% full BY VOLUME, with flat heads, so the barrel is the whole tank. Those two numbers only agree at the halfway mark — a horizontal tank is widest at the middle and narrows to nothing top and bottom, which is why a linearly marked dipstick is wrong everywhere else and why tanks come with a strapping table.

Tank capacity when full: 721.02 gal
Ullage — the empty space above: 504.48 gal
Depth as a proportion of the diameter: 34.04 %
Volume as a proportion of capacity: 30.03 %
In the cylindrical barrel: 216.54 gal

Then change the inputs to see how far the answer moves.

Show calculation logic

How this was calculated

Formula source(s)

The wetted cross-section of a horizontal cylinder is a circular segment, area r²·acos((r−h)/r) − (r−h)·√(2rh − h²). This is exact geometry rather than an approximation: it returns half the circle at half the diameter and the whole circle at full depth
Two hemispherical heads together form one sphere, and a sphere filled to depth h contains πh²(3r − h)/3. A 2:1 elliptical dished head is half the depth of a hemisphere and contributes half the volume, which is the standard treatment for the common pressure-vessel head
For fuel inventory, custody transfer or any regulated measurement, the governing figure comes from the tank's own calibrated STRAPPING TABLE rather than from geometry — a real tank is never exactly its drawing

Inputs used

Tank diameter: 47 in
Barrel length: 8 ft
Liquid depth: 16 in
Tank ends: Flat ends — a plain cylinder

Intermediate steps

Tank capacity when full: 721.02 gal
Ullage — the empty space above: 504.48 gal
Depth as a proportion of the diameter: 34.04 %
Volume as a proportion of capacity: 30.03 %
In the cylindrical barrel: 216.54 gal

Final result216.54 gal

Confidence note: The tank is 34% full BY DEPTH and 30% full BY VOLUME, with flat heads, so the barrel is the whole tank. Those two numbers only agree at the halfway mark — a horizontal tank is widest at the middle and narrows to nothing top and bottom, which is why a linearly marked dipstick is wrong everywhere else and why tanks come with a strapping table.

What this calculation does not cover

This is geometry, not gauging. A real tank is dented, out of round, sitting out of level or carrying sludge in the bottom, and none of that is in the arithmetic — for fuel inventory, custody transfer or any regulated measurement the governing figure is the tank's own calibrated strapping table.
A tank out of level is the commonest error and the hardest to see. Tilt moves the depth at one end relative to the other, and a dipstick at one end of a long tank then reports a depth the rest of the tank does not have. Measure at the middle, or measure both ends and check they agree.
The diameter wanted is the INTERNAL one. On a double-skinned or bunded tank the outer shell can be substantially larger than the vessel holding the liquid, and using it overstates every figure here.
Dished heads are treated as 2:1 elliptical, which is the common pressure-vessel proportion. Torispherical, flanged-and-dished and other profiles hold different amounts, and a manufacturer's drawing governs over this assumption.
Nothing here converts volume to mass. Fuel, oil and chemicals differ in density, and density itself moves with temperature — which is why a tank gauged warm and a tank gauged cold can hold the same volume and weigh differently.
The result is the liquid present, not the usable liquid. Most tanks draw from an outlet above the very bottom, so the last portion is unreachable, and a heating oil tank in particular should never be run down to what this figure says is left.

Estimated cost — your price

Price per gal ($)

This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.

Schematic, drawn to the proportions you entered — not to scale on screen.

Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.

Sources checked 2026-09-15 · v1.0.0

Regulatory standards & verification citations3

The wetted cross-section of a horizontal cylinder is a circular segment, area r²·acos((r−h)/r) − (r−h)·√(2rh − h²). This is exact geometry rather than an approximation: it returns half the circle at half the diameter and the whole circle at full depth
Two hemispherical heads together form one sphere, and a sphere filled to depth h contains πh²(3r − h)/3. A 2:1 elliptical dished head is half the depth of a hemisphere and contributes half the volume, which is the standard treatment for the common pressure-vessel head
For fuel inventory, custody transfer or any regulated measurement, the governing figure comes from the tank's own calibrated STRAPPING TABLE rather than from geometry — a real tank is never exactly its drawing

Cite this page

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How to calculate horizontal cylinder tank partial fill volume in 5 steps

Tank diameterThe internal diameter of the cylindrical barrel.
Barrel lengthThe straight cylindrical part, not counting the ends.
Liquid depthThe dipstick reading, measured from the lowest point inside the tank.
Tank endsFlat, dished, or fully hemispherical heads.
Liquid in the tankThe tool computes the liquid in the tank from those figures and shows the formula, its sources, and a confidence rating alongside it.

Liquid in the tank by tank diameter

Page defaults, not your figures above.

Tank diameter	Liquid in the tank (gal)
20 in	113
40 in	196
60 in	252
80 in	298

Frequently asked questions

Why is a dipstick reading not proportional to the contents?: Because a tank on its side is not the same width all the way up. At the halfway line it is at its widest — the full diameter — and it narrows to nothing at the very top and the very bottom. So the first inch of depth covers only a narrow strip along the bottom of the tank, while an inch either side of the centreline covers the full width. The consequence is easy to state and easy to get wrong in practice: a stick reading a QUARTER of the diameter is holding about a fifth of the contents, and a stick reading a TENTH is holding about a twentieth. The error runs the wrong way for anyone watching a heating oil tank get low, because it over-reports what is left just when the remaining amount matters most. The one place the intuition works is dead centre: half the depth really is half the volume, because the top half of a circle is the mirror image of the bottom half.
How much do the ends actually matter?: On a tank whose barrel is twice its diameter, two hemispherical heads hold about a quarter of the whole capacity, and the shorter the tank the more they matter. That is more than most people expect: two hemispherical heads are not two curved caps — put together they are one complete sphere of extra capacity. The common 2:1 elliptical dished head is half as deep as a hemisphere and contributes half as much, which is still not a rounding error. Ignoring the ends does not just make the capacity figure wrong; it makes it wrong in a way that varies with fill level, because the ends are also widest at the middle. If you are working from a manufacturer's capacity figure and your own barrel-only arithmetic disagrees with it, the heads are the first place to look.
What is ullage, and why is it the number some people want?: Ullage is the empty space above the liquid — capacity minus contents. It is the figure a delivery driver works to, because what matters at the filling point is how much more will fit, not how much is already there. It is also the safety number: many liquids need headspace for thermal expansion, and a tank filled to the brim on a cold morning can vent or deform by the afternoon. Some gauges are marked in ullage rather than contents for exactly this reason, measuring down from the top rather than up from the bottom, which is a real source of confusion when two people compare readings from the same tank. If your stick is measuring down from a fill point, the number you have is ullage and this page's depth input wants the other one.
When should I stop trusting this and use the tank's own table?: Whenever the number has consequences beyond planning. This page computes an ideal cylinder, and a real tank is not one: it may be dented, slightly out of round, resting out of level in its cradle, carrying years of sludge and water in the bottom, or fitted with internal baffles that displace liquid. Any of those makes the true contents differ from the geometry, and the difference is largest near the bottom — exactly where a low-level reading is being taken. For fuel inventory reconciliation, for custody transfer, or for anything a regulator will look at, the governing figure comes from the tank's calibrated strapping table, produced by measuring that individual vessel. Use this for checking a delivery looks sane, for planning, and for understanding why the stick is behaving as it is.

Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — a confirmed fix gets a permanent check of its own, so the same mistake cannot come back.