Why is a sphere's gauge worse than a cylinder's?

Because it narrows in two directions at once. A horizontal cylinder is the full length of the tank at every depth — only its width changes as you go up. A sphere has no such constant dimension: near the bottom it is narrow both across and along, so the same increment of depth covers a far smaller slice of liquid. The numbers make the point better than the description. A horizontal cylinder at a tenth of its diameter holds about five per cent of its contents; a sphere at a tenth of its diameter holds under three. At a quarter of the diameter the cylinder is near a fifth full and the sphere is not yet a sixth. Both then catch up and overshoot in the middle, and both are exactly half full at half the depth, because every shape symmetric about its equator is. The practical consequence is that a sphere's low-level reading is the least trustworthy number on any tank on a site.

Where can I actually trust a dipstick?

Through the straight barrel of a capsule, and nowhere else. In the cylindrical middle section the cross-section is a constant circle, so depth and volume are exactly proportional and a linearly marked stick is not an approximation — it is correct. The moment the liquid level drops into the lower head or rises into the upper one, the cross-section starts changing and the stick starts lying. That is why this page reports the barrel as a percentage of the tank's total height: it is the size of the band in which the simple reading works. On a vessel that is mostly heads, that band is small, and on a sphere it does not exist at all. It is also why serious installations gauge by pressure or by weight rather than by depth — both of those stay proportional to contents regardless of the shape the contents are sitting in.

Why does the page say a real vessel holds less than this?

Because it assumes true hemispherical heads and most pressure vessels do not have them. A hemisphere is the deepest possible head — its depth equals the radius — and it is also the most expensive to form, so it is used mainly where pressure is high or the vessel is large. Far more common are 2:1 elliptical heads, which are half as deep, and torispherical heads, which are shallower still. Both hold less than a hemisphere of the same diameter, so a real tank of the same stated diameter and barrel length has less capacity than this page computes, and the entire shortfall sits in the ends. If the manufacturer's capacity figure is lower than the number here and you cannot see why, the head profile is almost always the reason. The same caution applies to the partial-fill figures: near the top and bottom, where the heads are all there is, the error is proportionally at its largest.

Should I fill a tank to the capacity this gives?

No, and for a pressurised vessel that is a safety matter rather than a preference. LPG and similar liquids expand substantially with temperature, and a vessel filled liquid-full on a cold morning has nowhere for that expansion to go by the afternoon; the pressure relief valve is the last line of defence, not a design feature to be relied on. So filling is limited to a fixed proportion of capacity, with the remainder left as vapour space, and that limit — not the geometry — is the figure a filler works to. The same reasoning applies less dramatically to non-pressurised storage, where headspace absorbs thermal expansion and stops a tank venting or overflowing. Treat the capacity here as the volume the shell encloses, which is the starting point for a fill limit rather than a target.

Materials & Quantities

Sphere and Capsule Tank Volume Calculator

Contents of a spherical or vertical capsule tank at a measured depth, and why a dipstick only tells the truth through the straight middle.

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Every formula citedNamed published standards
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Market

Imperial · sales tax

Tank diameter

The internal diameter at the widest point.

Internal rather than external, and measured at the equator — the widest point of a sphere, or the barrel of a capsule. On an insulated or jacketed vessel the outside is substantially larger than the space holding the liquid.

Tank shape

A plain sphere, or a straight barrel capped at both ends.

The two are the same geometry with and without a middle: a sphere is a capsule whose barrel has zero length. Choosing sphere makes the barrel length below irrelevant, and the page says so rather than silently ignoring it.

Straight barrel length

The straight cylindrical section between the two heads.

Seam to seam, excluding the heads, because the heads are counted separately. This is the only part of the tank where depth and volume are proportional, so its length is also the height of the band in which a dipstick can be trusted.

Liquid depth

Measured from the lowest point inside the tank.

From the inside bottom of the lower head, not from the ground or from a skirt. On a vessel standing on legs the difference is the whole height of the legs, and on a sphere the lowest internal point is not where the shell touches its support ring.

Contents at this depth

492.6 gal

High confidence

33% full BY DEPTH, 30% BY VOLUME. This reading is inside the straight barrel, where depth and volume ARE proportional and a dipstick is exact. The barrel is 55% of the tank's height, and it is the only part of it a linearly marked stick describes honestly.

Capacity when full: 1,619.35 gal
Ullage — the empty space above: 1,126.8 gal
Depth as a proportion of the height: 33.33 %
Volume as a proportion of capacity: 30.42 %
Height of the band a dipstick reads honestly: 55.32 %

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

Show calculation logic

How this was calculated

Formula source(s)

A sphere of radius r filled to depth h contains πh²(3r − h)/3 — the standard spherical cap, which returns a hemisphere at h = r and a whole sphere at h = 2r. Both boundaries are checked rather than assumed
Above the equator the filled region is a spherical zone, πt(r² − t²/3) for a height t above the widest point, which returns the upper hemisphere exactly at t = r. A vertical capsule is that pair of heads with a straight cylinder between them, so one expression family covers both shapes and a sphere is simply a capsule with no barrel
For fuel inventory, custody transfer or any regulated measurement, the governing figure is the vessel's own calibrated strapping table. A pressure vessel's heads are frequently torispherical rather than hemispherical, which holds less

Inputs used

Tank diameter: 63 in
Tank shape: Vertical capsule — a straight barrel with hemispherical heads
Straight barrel length: 6.5 ft
Liquid depth: 47 in

Intermediate steps

Capacity when full: 1,619.35 gal
Ullage — the empty space above: 1,126.8 gal
Depth as a proportion of the height: 33.33 %
Volume as a proportion of capacity: 30.42 %
Height of the band a dipstick reads honestly: 55.32 %

Final result492.55 gal

Confidence note: 33% full BY DEPTH, 30% BY VOLUME. This reading is inside the straight barrel, where depth and volume ARE proportional and a dipstick is exact. The barrel is 55% of the tank's height, and it is the only part of it a linearly marked stick describes honestly.

What this calculation does not cover

This is geometry, not gauging. For fuel inventory, custody transfer or any regulated measurement the governing figure is the vessel's own calibrated strapping table, produced by measuring that individual tank.
The heads are taken as true hemispheres. Most pressure vessels use torispherical or 2:1 elliptical heads instead, which are shallower and hold LESS — so a real vessel of the same diameter and barrel length holds less than this page says, and the shortfall is entirely in the ends.
A sphere's supports sit below its lowest internal point, and a vertical vessel's skirt or legs sit below its lower head. Depth measured from the ground rather than from the inside bottom overstates the contents by that whole height.
Nothing here converts volume to mass, and for LPG that gap matters more than usual: the liquid's density changes substantially with temperature, so the same depth is a different weight on a hot afternoon than on a cold morning.
Pressurised vessels are never filled to their geometric capacity. A fill limit — commonly a fixed percentage — leaves vapour space for expansion, and that limit rather than this figure is the number a filler works to.
The result is the liquid present, not the usable liquid. A draw-off above the very bottom leaves a heel that cannot be taken out, and on a sphere that heel is a surprisingly small volume for its depth.

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

A sphere of radius r filled to depth h contains πh²(3r − h)/3 — the standard spherical cap, which returns a hemisphere at h = r and a whole sphere at h = 2r. Both boundaries are checked rather than assumed
Above the equator the filled region is a spherical zone, πt(r² − t²/3) for a height t above the widest point, which returns the upper hemisphere exactly at t = r. A vertical capsule is that pair of heads with a straight cylinder between them, so one expression family covers both shapes and a sphere is simply a capsule with no barrel
For fuel inventory, custody transfer or any regulated measurement, the governing figure is the vessel's own calibrated strapping table. A pressure vessel's heads are frequently torispherical rather than hemispherical, which holds less

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Most jobs need more than one number. Add the calculators you need next and they open right here, underneath this one — your figures stay on screen and nothing is lost to a page change.

How to calculate sphere and capsule tank volume in 5 steps

Tank diameterThe internal diameter at the widest point.
Tank shapeA plain sphere, or a straight barrel capped at both ends.
Straight barrel lengthThe straight cylindrical section between the two heads.
Liquid depthMeasured from the lowest point inside the tank.
Contents at this depthThe tool computes the contents at this depth from those figures and shows the formula, its sources, and a confidence rating alongside it.

Contents at this depth by tank diameter

Page defaults, not your figures above.

Tank diameter	Contents at this depth (gal)
40 in	221
60 in	456
80 in	738
100 in	1,040
120 in	1,343

Frequently asked questions

Why is a sphere's gauge worse than a cylinder's?: Because it narrows in two directions at once. A horizontal cylinder is the full length of the tank at every depth — only its width changes as you go up. A sphere has no such constant dimension: near the bottom it is narrow both across and along, so the same increment of depth covers a far smaller slice of liquid. The numbers make the point better than the description. A horizontal cylinder at a tenth of its diameter holds about five per cent of its contents; a sphere at a tenth of its diameter holds under three. At a quarter of the diameter the cylinder is near a fifth full and the sphere is not yet a sixth. Both then catch up and overshoot in the middle, and both are exactly half full at half the depth, because every shape symmetric about its equator is. The practical consequence is that a sphere's low-level reading is the least trustworthy number on any tank on a site.
Where can I actually trust a dipstick?: Through the straight barrel of a capsule, and nowhere else. In the cylindrical middle section the cross-section is a constant circle, so depth and volume are exactly proportional and a linearly marked stick is not an approximation — it is correct. The moment the liquid level drops into the lower head or rises into the upper one, the cross-section starts changing and the stick starts lying. That is why this page reports the barrel as a percentage of the tank's total height: it is the size of the band in which the simple reading works. On a vessel that is mostly heads, that band is small, and on a sphere it does not exist at all. It is also why serious installations gauge by pressure or by weight rather than by depth — both of those stay proportional to contents regardless of the shape the contents are sitting in.
Why does the page say a real vessel holds less than this?: Because it assumes true hemispherical heads and most pressure vessels do not have them. A hemisphere is the deepest possible head — its depth equals the radius — and it is also the most expensive to form, so it is used mainly where pressure is high or the vessel is large. Far more common are 2:1 elliptical heads, which are half as deep, and torispherical heads, which are shallower still. Both hold less than a hemisphere of the same diameter, so a real tank of the same stated diameter and barrel length has less capacity than this page computes, and the entire shortfall sits in the ends. If the manufacturer's capacity figure is lower than the number here and you cannot see why, the head profile is almost always the reason. The same caution applies to the partial-fill figures: near the top and bottom, where the heads are all there is, the error is proportionally at its largest.
Should I fill a tank to the capacity this gives?: No, and for a pressurised vessel that is a safety matter rather than a preference. LPG and similar liquids expand substantially with temperature, and a vessel filled liquid-full on a cold morning has nowhere for that expansion to go by the afternoon; the pressure relief valve is the last line of defence, not a design feature to be relied on. So filling is limited to a fixed proportion of capacity, with the remainder left as vapour space, and that limit — not the geometry — is the figure a filler works to. The same reasoning applies less dramatically to non-pressurised storage, where headspace absorbs thermal expansion and stops a tank venting or overflowing. Treat the capacity here as the volume the shell encloses, which is the starting point for a fill limit rather than a target.

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.