Cone-Bottom Tank Volume Calculator
Work out the volume and capacity of a cone-bottom (conical-bottom) tank — a cylinder sitting above a cone-shaped bottom — in US gallons, imperial gallons, litres, cubic feet and cubic metres. Enter the cylinder diameter and height, the cone height and the cone-tip diameter for the total capacity, or turn on partial fill to see how much liquid is in a part-full tank.
Tank volume calculator
What is a cone-bottom tank?
A cone-bottom tank — also called a conical-bottom tank — is a cylindrical tank whose base tapers down to a cone (more precisely a frustum, a cone with the tip cut to a small opening). The sloped bottom lets the tank drain completely, which is why cone-bottom tanks are common for slurries, powders, dairy, brewing and chemical mixing. To find its capacity you add two parts together: the cylinder on top and the cone/frustum beneath it.
Cone-bottom tank volume formula
The total cone bottom tank volume is the cylinder volume plus the frustum volume:
where R is the cylinder radius (half the cylinder diameter), H is the cylinder height, h is the cone height, and r is the radius of the cone tip — the small lower opening. The first term is the cylindrical section; the second is the conical bottom. If the cone tapers to a true point, set the tip diameter to a very small value and the frustum term approaches the simple cone volume (π h / 3) R². For the derivations and sources behind every formula on this site, see the methodology page.
How a cone-bottom tank fills (partial fill order)
Liquid fills a cone-bottom tank from the very bottom upward, so the order is:
- The cone/frustum bottom fills first. While the liquid level is still within the cone, the filled volume is the part-full frustum from the tip up to the liquid height, and the radius of the liquid surface grows as the level rises.
- The cylindrical section fills after the cone is full. Once the level reaches the top of the cone, the cone is completely full and the straight cylindrical section above begins to fill linearly with height.
Measure the liquid level from the bottom tip of the cone. The calculator handles the transition from cone to cylinder automatically.
Worked example
Take a cone-bottom tank with a cylinder diameter of 5 ft (so R = 2.5 ft), cylinder height H = 6 ft, cone height h = 3 ft, and cone-tip diameter 1 ft (so r = 0.5 ft).
- Cylinder volume: π × 2.5² × 6 = 117.81 ft³.
- Cone (frustum) volume: (π × 3 / 3) × (2.5² + 2.5 × 0.5 + 0.5²) = π × (6.25 + 1.25 + 0.25) = 24.35 ft³.
- Total: 117.81 + 24.35 = 142.16 ft³ ≈ 1,064 US gallons (≈ 886 imperial gallons, ≈ 4,026 litres).
- Cone just full (liquid height = 3 ft): the filled volume equals the frustum, 24.35 ft³ ≈ 182 US gallons — after this point the cylinder begins to fill.
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
This calculator reports cone bottom tank capacity in US gallons, imperial (UK) gallons, litres, cubic feet and cubic metres at once, 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
For a plain cylinder with flat ends, use the vertical cylindrical or horizontal cylindrical tank volume calculator. Cone-top tanks (which fill the cylinder first and the cone last) and plain cone/frustum tanks are also available on the main tank volume calculator — choose the matching shape from the dropdown.
Frequently asked questions
How do you calculate the volume of a cone-bottom tank?
A cone-bottom tank is a cylinder sitting on top of a cone (frustum) bottom, so its total volume is the cylinder volume plus the cone-bottom volume: V = πR²H + (πh/3)(R² + Rr + r²), where R is the cylinder radius, H the cylinder height, h the cone height, and r the radius of the cone tip (the small lower opening). Enter those dimensions above and the calculator returns the capacity in every common unit.
What is the cone-bottom tank volume formula?
V = πR²H + (πh/3)(R² + Rr + r²). The first term is the cylindrical section; the second is the conical (frustum) bottom, using the larger radius R where it meets the cylinder and the smaller radius r at the tip. If the cone comes to a full point, r = 0 and the second term reduces to the simple cone volume (πh/3)R².
How does a cone-bottom tank fill?
From the bottom up, the cone (frustum) fills first. Only once the conical bottom is completely full does the cylindrical section above start to fill. The calculator follows this fill order: enter a liquid level measured from the very bottom (the cone tip) and it reports the filled and empty volumes correctly across the cone-to-cylinder transition.
How do I work out cone-bottom tank capacity at a partial level?
Turn on “Calculate partial fill” and enter the liquid height from the bottom tip. While the level is within the cone, the filled volume is the part-full frustum from the tip up to that height; once the level passes the top of the cone, it is the full cone plus the cylindrical volume above it. The result is shown in US gallons, imperial gallons, litres, cubic feet and cubic metres.
What is the difference between a cone-bottom and a cone-top tank?
They share the same total volume for the same dimensions, but they fill in opposite order. A cone-bottom tank fills the cone first and the cylinder afterwards; a cone-top tank fills the cylinder first and the cone last. This page models the cone-bottom case. Cone-top and plain cone/frustum tanks are handled on the main tank volume calculator.
Why use inside dimensions?
The calculator computes the volume of an ideal cylinder-plus-cone from the numbers you enter and does not account for wall thickness, the support skirt or legs, internal fittings, or a rounded cone-to-cylinder weld. Enter inside dimensions for the closest estimate of actual liquid capacity.