Spherical Tank Volume Calculator
Work out the volume and capacity of a spherical tank — a true sphere, as used for pressurised gas and cryogenic storage — in US gallons, imperial gallons, litres, cubic feet and cubic metres. Enter the diameter for the total capacity, or turn on partial fill to find how much liquid is in a part-full sphere.
Tank volume calculator
How to calculate spherical tank volume
A spherical tank is a complete sphere, so its capacity depends only on one measurement: the inside diameter. The volume of a spherical tank is:
where r is the inside radius. If you know the diameter d instead, use r = d / 2, giving the same spherical tank volume formula written as V = (4/3) × π × (d / 2)³. Because the radius is cubed, a small change in diameter makes a large change in capacity — doubling the diameter multiplies the volume by eight.
Partial fill uses the spherical cap formula
Unlike a box or an upright cylinder, a sphere does not fill in proportion to height: it is narrow at the bottom, widest at the middle, and narrow again at the top. The liquid forms a spherical cap, so the volume of a partially filled spherical tank at a liquid height h measured from the bottom is:
Two checks confirm the formula: at h = r (filled to the equator, half the diameter) the tank is exactly half full, and at h = 2r it is completely full. For the derivations and sources behind every formula on this site, see the methodology page.
Worked example
Take a spherical tank with a diameter of 5 ft (so r = 2.5 ft).
- Total volume: V = (4/3) × π × 2.5³ = 65.45 ft³. At 7.48052 US gallons per cubic foot, that is about 490 US gallons (≈ 408 imperial gallons, ≈ 1,853 litres).
- Half full (liquid height = 2.5 ft): V = π × 2.5² × (3 × 2.5 − 2.5) / 3 = 32.72 ft³ ≈ 245 US gallons — exactly half the total, because the equator is the half-way line of a sphere.
- Quarter height (liquid height = 1.25 ft): V = π × 1.25² × (3 × 2.5 − 1.25) / 3 = 9.20 ft³ ≈ 69 US gallons — only about 14% of capacity, not 25%, because the sphere is narrow near the bottom.
Enter these numbers in the calculator above to confirm the figures and read off imperial gallons, litres, cubic feet and cubic metres at the same time.
Spherical, hemispherical and capsule tanks
These related shapes are easy to mix up:
- A spherical tank is a full sphere — this page, using V = (4/3)πr³.
- A hemispherical tank is half-sphere geometry: a dome or bowl. Its volume is half a sphere, V = (2/3)πr³, which is the spherical cap formula evaluated at h = r.
- A cylindrical tank with hemispherical ends is a capsule tank — a straight cylinder body with a half-sphere on each end, which together make one sphere. For that shape use the capsule tank volume calculator.
Units and gallons
This spherical tank capacity calculator reports every common unit at once: 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 the inside diameter for the closest estimate of liquid capacity.
Other tank shapes
A “round tank” or “circular tank” is usually an upright cylinder, not a sphere — for those use the vertical cylindrical tank volume calculator. For a cylinder lying on its side, use the horizontal cylindrical tank volume calculator. For capsule, 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 spherical tank?
Use V = (4/3) × π × r³, where r is the inside radius (half the diameter). The full capacity of a spherical tank depends only on its diameter. The calculator above does this from the diameter you enter and shows the result in US gallons, imperial gallons, litres, cubic feet and cubic metres at once.
What is the spherical tank volume formula?
For a full sphere the volume is V = (4/3) × π × r³. If you know the diameter d rather than the radius, use r = d / 2, giving V = (4/3) × π × (d / 2)³. Keep dimensions in the same unit, then convert to gallons or litres — or let the calculator convert for you.
How do I find the volume of a partially filled spherical tank?
A sphere does not fill linearly with height. The liquid forms a spherical cap, so the filled volume at liquid height h measured from the bottom is V = π × h² × (3r − h) / 3. At h = r (half the diameter) the tank is exactly half full; at h = 2r it is full. Turn on “Calculate partial fill”, enter the liquid level, and the calculator reports the filled and empty volumes.
What is the difference between a spherical tank and a hemispherical tank?
A spherical tank is a complete sphere — common for pressurised LPG, LNG and other gas storage because a sphere spreads pressure evenly. A hemispherical tank is half that geometry (a dome or bowl). The partial-fill maths on this page is built from the spherical cap formula, which is the same building block used for hemispherical shapes and for the rounded ends of a capsule tank.
Is a spherical tank the same as a round or circular tank?
No. “Round tank” and “circular tank” almost always mean an upright cylinder with a circular base — use the vertical cylindrical tank volume calculator for those. A spherical tank is a true sphere (ball-shaped), so it uses V = (4/3)πr³ and fills as a spherical cap rather than linearly with height.
What units does this spherical tank calculator output?
Results appear simultaneously 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 the diameter in US units (feet and inches) or metric (metres and centimetres) using the toggle.