Conical Tank Volume Calculator
Work out the volume and capacity of a conical tank — a cone or a truncated cone (frustum) — in US gallons, imperial gallons, litres, cubic feet and cubic metres. Enter the top diameter, bottom diameter and height for the total capacity, or turn on partial fill to find how much liquid is in a part-full tank. Works for upright and inverted cones alike.
Tank volume calculator
How to calculate conical tank volume
A conical tank is a cone — or, almost always in practice, a frustum: a cone with the tip cut off so it has a larger circle at one end and a smaller circle at the other. The volume of a conical tank is:
where h is the height, R is the larger radius and r is the smaller radius (each is half the corresponding diameter). This is the conical tank volume formula for a truncated cone. If the tank tapers to a true point, then r = 0 and it simplifies to the classic cone volume:
In other words, a full cone holds exactly one third of the cylinder that would enclose it. For the derivations and sources behind every formula on this site, see the methodology page.
Upright and inverted conical tanks
“Conical tank” covers both orientations. An upright cone is wider at the bottom and narrows toward the top; an inverted conical tank is wider at the top and narrows toward the bottom — common for hoppers and draining vessels. The total volume is identical either way; only the partial-fill behaviour changes. Enter the actual top and bottom diameters as they are on your tank and the calculator does the rest.
Cone vs frustum (truncated cone)
A cone tapers to a single point; a frustum is that cone with the tip removed, leaving a small flat circular face. Real conical tanks are nearly always frustums, because a perfect point cannot hold an outlet or fitting. This calculator uses the frustum formula, which covers both: set the smaller diameter close to zero for a near-perfect cone, or to its true value for a truncated cone.
Partial fill in a conical tank
Because the cross-section changes with height, a conical tank does not fill proportionally to depth. The liquid in the bottom forms its own smaller cone or frustum, so a given rise in level adds different amounts of volume depending on how full the tank already is. The calculator computes the exact part-full frustum from the bottom up to the liquid level — just turn on “Calculate partial fill” and enter the liquid height.
Worked example
Take a conical (truncated-cone) tank with a top diameter of 2 ft (so r = 1 ft), a bottom diameter of 5 ft (so R = 2.5 ft) and a height of 6 ft.
- Total volume: V = (π × 6 / 3) × (2.5² + 2.5 × 1 + 1²) = 2π × (6.25 + 2.5 + 1) = 2π × 9.75 = 61.26 ft³ ≈ 458 US gallons (≈ 382 imperial gallons, ≈ 1,735 litres).
- Half height (liquid height = 3 ft): the surface radius is 1.75 ft, giving a part-full frustum of about 43.0 ft³ ≈ 322 US gallons — about 70% of the total, because this tank is wider at the bottom and so fills faster low down.
Enter these numbers in the calculator above 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.
Related tank shapes
If your tank is a cylinder with a cone on the bottom or top rather than an all-cone body, use the cone-bottom tank volume calculator or the cone-top tank volume calculator. For plain cylinders, see the vertical and horizontal cylindrical tank calculators, or the main tank volume calculator for every shape.
Frequently asked questions
How do you calculate the volume of a conical tank?
Most conical tanks are truncated cones (frustums), with one diameter at the top and another at the bottom. The volume is V = (πh/3)(R² + Rr + r²), where h is the height, R is the larger radius and r is the smaller radius. For a tank that comes to a true point, the small radius is zero and this reduces to the simple cone volume V = (πh/3)R². Enter the top and bottom diameters and the height above and the calculator returns the capacity in every common unit.
What is the conical tank volume formula?
For a truncated cone (frustum): V = (πh/3)(R² + Rr + r²), using the top radius and bottom radius. For a full cone tapering to a point: V = (πh/3)R² = (1/3) × π × radius² × height — one third of the cylinder that would enclose it. The calculator uses the frustum form, which covers both cases.
Does this work for an inverted conical tank?
Yes. An inverted cone is simply wider at the top than at the bottom. Enter the larger measurement as the top diameter and the smaller as the bottom diameter. The volume is the same whichever way up the cone sits; only the partial-fill behaviour changes, and the calculator accounts for the orientation you enter.
How do I find the volume of liquid in a partially filled conical tank?
Turn on “Calculate partial fill” and enter the liquid height measured from the bottom. Because the cross-section widens (or narrows) with height, the filled volume is itself a smaller cone or frustum from the bottom up to the liquid level — it is not proportional to depth. The calculator computes this exactly and reports the filled and empty volumes.
What is the difference between a cone and a frustum?
A cone tapers to a single point; a frustum is a cone with the tip cut off, leaving a smaller circular face. Real “conical” tanks are almost always frustums, because a perfect point cannot hold a fitting or outlet. This page handles both: set the smaller diameter to nearly zero for a near-perfect cone, or to its real value for a truncated cone.
What units does the conical 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.