Capsule Tank Volume Calculator
Work out the volume and capacity of a capsule (bullet) tank — a cylinder with a hemispherical cap on each end — in US gallons, imperial gallons, litres, cubic feet and cubic metres. This one page covers both horizontal and vertical capsule tanks. Enter the diameter and straight side length, and switch the shape selector to match your tank’s orientation.
Tank volume calculator
Horizontal and vertical capsule tanks on one page
A capsule tank is a cylinder closed off by a hemisphere at each end — the rounded “bullet” shape used for propane, anhydrous ammonia and other pressurised liquids. This page handles both orientations:
- Horizontal capsule — lying on its side. This is the calculator’s default.
- Vertical capsule — standing upright. Switch the “Tank shape” dropdown to “Vertical capsule” if that matches your tank.
For the same diameter and straight side length, both orientations have exactly the same total volume; only the partial-fill behaviour differs.
Capsule tank volume formula
The total volume of a capsule tank is the cylinder in the middle plus the two hemispherical ends. Because two hemispheres make one full sphere, the capsule tank volume formula is:
where r is the inside radius (half the diameter) and a is the straight side length of the cylindrical section. The first term, π r² a, is the cylinder; the second term, (4/3) π r³, is the sphere formed by the two end caps. An equivalent compact form is V = π r² ( (4/3) r + a ). For the derivations and sources behind every formula on this site, see the methodology page.
Partial fill differs by orientation
The total is orientation-independent, but how the tank fills is not:
- Horizontal capsule — the cylindrical body fills as a circular segment (exactly like a horizontal cylinder), while the two end caps together fill as a single sphere. Depth and volume are not proportional.
- Vertical capsule — the liquid fills in three stages: the bottom hemisphere first, then the cylindrical section (which fills linearly with height), then the top hemisphere. The calculator blends these regions smoothly.
Worked example
Take a capsule tank with a diameter of 4 ft (so r = 2 ft) and a straight side length of 8 ft.
- Total volume: cylinder = π × 2² × 8 = 100.53 ft³; sphere = (4/3) × π × 2³ = 33.51 ft³. Total = 134.04 ft³ ≈ 1,003 US gallons (≈ 835 imperial gallons, ≈ 3,795 litres). This total is the same whether the tank is horizontal or vertical.
- Horizontal, half full (liquid depth = 2 ft, the centre line): by symmetry the tank holds exactly half its total, about 502 US gallons.
- Vertical, filled to the top of the bottom hemisphere (liquid height = 2 ft = r): that is one hemisphere = (2/3) × π × 2³ = 16.76 ft³ ≈ 125 US gallons, after which the cylindrical section begins to fill linearly.
Enter these numbers in the calculator above, switching between the horizontal and vertical capsule options, to confirm the figures and read imperial gallons, litres, cubic feet and cubic metres at the same time.
Units and gallons
Results appear at once in US gallons, imperial (UK) gallons, litres, cubic feet and cubic metres, plus optional petroleum barrels. One US liquid gallon is 231 cubic inches ≈ 3.785 litres, while one imperial gallon ≈ 4.546 litres, so both are shown to avoid ambiguity. Enter inside dimensions for the closest estimate of liquid capacity.
Other tank shapes
If your tank has flat ends rather than hemispherical caps, use the horizontal cylindrical or vertical cylindrical tank volume calculator instead. For rectangular, oval, elliptical and cone-shaped tanks, the main tank volume calculator handles every supported tank shape with full and partial-fill results.
Frequently asked questions
How do you calculate the volume of a capsule tank?
A capsule is a cylinder with a hemispherical cap on each end. The two hemispheres together make a full sphere, so the total volume is the cylinder plus one sphere: V = πr²a + (4/3)πr³, where r is the radius and a is the straight side (cylinder) length. Enter the diameter and straight side length above and the calculator returns the capacity in every common unit.
What is the capsule tank volume formula?
V = πr²a + (4/3)πr³. The first term is the cylindrical middle section of length a; the second is the sphere formed by the two hemispherical end caps. An equivalent compact form is V = πr²((4/3)r + a). Orientation — horizontal or vertical — does not change the total volume.
Does a horizontal and vertical capsule tank hold the same volume?
Yes. For the same diameter and straight side length, a horizontal capsule and a vertical capsule have exactly the same total capacity. What changes with orientation is partial fill — how the volume builds up as the liquid level rises.
How does partial fill work for a horizontal capsule?
Lying on its side, the cylindrical body fills as a circular segment (like a horizontal cylinder), and the two end caps together fill as a single sphere. The relationship between liquid depth and volume is not linear: near the middle of the tank an inch of depth adds the most volume. Turn on “Calculate partial fill” and enter the liquid level to get the filled and empty volumes.
How does partial fill work for a vertical capsule?
Standing upright, the tank fills in three stages: first the bottom hemisphere, then the cylindrical middle section (which fills linearly with height), then the top hemisphere. The calculator handles the transitions between these regions automatically. Switch the shape selector to “Vertical capsule” to model this case.
What units does the capsule tank calculator output?
Every result appears at once in US gallons, imperial (UK) gallons, litres, cubic feet and cubic metres, with an option to show petroleum barrels. One US liquid gallon is 231 cubic inches ≈ 3.785 litres; one imperial gallon ≈ 4.546 litres. Enter inside dimensions for the closest estimate of liquid capacity.