Conical Bottom Tank Volume Calculator & Formula

This calculator works out the volume of a conical-bottom tank (a cylinder with a cone or truncated cone at the bottom) from the cylinder diameter, cylinder height, cone bottom height, and bottom outlet diameter. You enter those dimensions in your preferred units, and it returns the total volume in cubic meters, liters, and US gallons, plus the separate volumes of the cylindrical and conical sections.

Formula

The total volume V of a conical-bottom tank is the sum of the cylindrical section and the conical (or frustum) section:

V = (π × D² / 4 × H) + (π × Hc / 12 × (D² + D × d + d²))

Where:

• D = diameter of the cylindrical section (same as the top diameter of the cone), in meters (m)
• H = height of the cylindrical section, in meters (m)
• Hc = height of the conical bottom (vertical distance from the cylinder bottom to the outlet), in meters (m)
• d = diameter of the bottom outlet (if the cone comes to a point, d = 0), in meters (m)

All dimensions must be in the same unit. The first term is the volume of a cylinder; the second term is the volume of a conical frustum (a cone with the tip cut off). If the bottom is a full cone (d = 0), the second term simplifies to (π × Hc × D² / 12), which is one-third of the volume of a cylinder of the same height.

Worked Example

Using the default values: D = 2.0 m, H = 3.0 m, Hc = 0.6 m, d = 0.2 m.

1. Cylinder volume = π × (2.0)² / 4 × 3.0 = π × 1.0 × 3.0 = 9.425 m³
2. Cone bottom volume = π × 0.6 / 12 × (2.0² + 2.0 × 0.2 + 0.2²) = 0.1571 × (4.0 + 0.4 + 0.04) = 0.1571 × 4.44 = 0.697 m³
3. Total volume = 9.425 + 0.697 = 10.122 m³
4. In liters: 10.122 × 1000 = 10,122 L
5. In US gallons: 10.122 × 264.172 = 2,674.2 gal

The calculator rounds the total to 10.122 m³, which matches the manual calculation.

When to Use This Calculator

Conical-bottom tanks are common in food processing, breweries, wineries, pharmaceuticals, and chemical storage because the sloped bottom allows complete drainage and easier cleaning. You need this volume calculation when:

• Determining the maximum capacity of a new or existing tank
• Mixing ingredients where the recipe is based on total batch volume
• Calculating the volume of liquid at a partial fill (see the section on partial fills below)
• Estimating the weight of contents (multiply volume by liquid density)

The result gives the total volume to the top of the cylindrical section. If the tank has a domed top or an overflow line, you may need to adjust the height accordingly.

How to Read the Result

The primary output is the total volume in cubic meters. For practical use, the calculator also provides:

• Cylinder volume – the volume of the straight-walled section
• Cone bottom volume – the volume of the sloped bottom
• Liters – useful for metric liquid measurements
• US gallons – useful for US customary units

Remember that the volume is the total capacity when filled to the top of the cylinder. If you need the volume at a specific fill height, you must calculate the partial volume, which is more complex because the cone fills first.

Common Mistakes and How to Avoid Them

• Mixing units – Always convert all dimensions to the same unit before entering them. If you measure in inches, convert to meters (1 in = 0.0254 m) or use a consistent unit and adjust the formula accordingly.
• Using the wrong cone formula – Many people use the full cone formula (V = πr²h/3) even when the bottom has a flat outlet. The frustum formula above is correct for a truncated cone.
• Forgetting the outlet diameter – If the bottom outlet is not a sharp point, ignoring it overestimates the volume. The error is small when d is much smaller than D, but it matters for accurate dosing.
• Rounding intermediate results – Keep full precision during calculations and round only at the end. The calculator does this automatically.

Limitations and Real-World Considerations

This calculator assumes perfect geometric shapes: a straight cylinder and a conical frustum with straight walls. Real tanks may have:

• Slight wall thickness (the internal diameter is smaller than the external)
• Dished or elliptical heads instead of flat tops
• Internal baffles, agitators, or heating coils that displace volume
• Insulation or lining that reduces the internal volume

For precise capacity, measure the internal dimensions. Also, the volume calculation does not account for the liquid’s thermal expansion or the fact that some liquids foam or leave a heel. Always leave a safety margin below the overflow point.

Partial Fill Volume

Often you need the volume at a certain liquid level, not just the full capacity. For a conical-bottom tank, the liquid first fills the cone, then the cylinder. To compute the volume at a given height h (measured from the bottom outlet):

• If h ≤ Hc (liquid is entirely in the cone): the liquid surface diameter is d + (D – d) × (h / Hc). Use the frustum formula with that diameter as the top diameter.
• If h > Hc (liquid fills the cone and part of the cylinder): add the full cone volume to the cylinder volume up to height (h – Hc).

This is more involved, but the same geometric principles apply. Many tank monitoring systems use a level sensor and a calibration table derived from these formulas.

Frequently Asked Questions

What is the difference between a conical bottom and a flat bottom tank?

A flat-bottom tank has a flat base, so it holds slightly more volume for the same height and diameter, but it cannot be drained completely without a sump or pump. A conical bottom slopes to a central outlet, allowing full drainage and easier cleaning, which is why it is preferred for sanitary and food applications.

How do I calculate the volume if my cone comes to a point?

If the bottom outlet diameter is zero (a perfect point), use the frustum formula with d = 0. The cone volume becomes (π × Hc × D²) / 12, which is exactly one-third of the volume of a cylinder of the same height and diameter.

Can I use this calculator for a tank with a dished bottom?

No. A dished (elliptical or torispherical) head has a different shape and requires a separate formula. This calculator is only for straight conical or truncated-conical bottoms.

Does the calculator work for any unit?

The calculator uses meters for the default, but you can enter any unit as long as you are consistent. If you enter all dimensions in feet, the result will be in cubic feet, not cubic meters. The liters and gallons outputs assume the input is in meters, so for other units you must convert manually.

Why do I need the outlet diameter?

The outlet diameter determines whether the bottom is a full cone or a truncated cone. A truncated cone has a flat bottom, which reduces the volume slightly compared to a sharp point. Including it gives a more accurate capacity, especially when the outlet is large relative to the tank diameter.

How accurate is this calculator for real tanks?

It is as accurate as your measurements. If you measure the internal dimensions correctly and the tank is a true cylinder with a straight conical bottom, the error is typically less than 1%. Real-world factors like wall thickness, internal fittings, and manufacturing tolerances can cause small deviations.

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in d | Cylinder diameter | m | 2.0 | 0
in h | Cylinder height | m | 3.0 | 0
in hc | Cone bottom height | m | 0.6 | 0
in d2 | Bottom outlet diameter | m | 0.2 | 0
out vol_total | Total volume | m³ | (pi * d^2 / 4 * h) + (pi * hc / 12 * (d^2 + d * d2 + d2^2)) | 3
out vol_cyl | Cylinder volume | m³ | pi * d^2 / 4 * h | 3
out vol_cone | Cone bottom volume | m³ | pi * hc / 12 * (d^2 + d * d2 + d2^2) | 3
out liters | Total volume in liters | L | vol_total * 1000 | 0
out gallons | Total volume in US gallons | gal | vol_total * 264.172 | 1