Cubic Feet Calculator: Cylinder Volume

This calculator works out the volume of a cylinder in cubic feet. You enter the cylinder’s diameter (or radius) and its height or length, and the result is the volume in cubic feet (ft³). It is useful for sizing air tanks, pipes, concrete columns, or any cylindrical container when you need the volume in imperial units.

Formula

The volume of a cylinder is the area of its circular base multiplied by its height. The formula is:

V = π × r² × h

Where:

• V = volume in cubic feet (ft³)
• Ï€ (pi) ≈ 3.14159
• r = radius of the circular base in feet (ft) – half the diameter
• h = height or length of the cylinder in feet (ft)

If you only have the diameter (d), use r = d/2. The calculator above does that automatically. If you measure in inches, convert to feet first by dividing by 12.

Worked Example

Using the default values from the calculator: diameter = 2 ft, height = 3 ft.

1. Radius r = diameter / 2 = 2 / 2 = 1 ft
2. Base area = π × r² = π × 1² = π ≈ 3.14159 ft²
3. Volume = base area × height = 3.14159 × 3 = 9.42477 ft³
4. Rounded to two decimals: 9.42 ft³

The calculator’s first output shows 9.42 ft³, matching this step-by-step calculation. The second output converts that volume to US gallons: 9.42 × 7.48052 ≈ 70.5 gallons.

When to Use a Cylinder Volume Calculation

You need this calculation whenever you are filling, emptying, or designing a cylindrical space and the result must be in cubic feet. Common situations include:

• Air receiver tanks – sizing a compressed air tank for a workshop or garage.
• Concrete columns or footings – estimating how much concrete to order for round pillars.
• Pipes and culverts – knowing the internal volume of a pipe for flow or storage calculations.
• Propane or fuel tanks – comparing tank sizes when the label only gives dimensions.
• Water storage – checking how much water a cylindrical cistern or rain barrel holds.

In many of these cases you may also want the volume in gallons or litres. One cubic foot equals 7.48052 US gallons, and one cubic foot equals 28.3168 litres. The calculator includes the US gallon conversion for convenience.

How to Measure a Cylinder Correctly

Getting accurate dimensions is the most important step. Here are the practical points:

• Use the inside diameter for capacity – the wall thickness reduces the usable volume. For a pipe, measure the inner diameter, not the outer.
• Measure height perpendicular to the base – if the cylinder is tilted, the height changes. For a horizontal tank, use the length of the tank as the height in the formula.
• Convert all units to feet before calculating – if you measure in inches, divide by 12. If you measure in centimetres, divide by 30.48.
• For partially filled tanks – the formula above gives total volume. For the volume of liquid at a certain depth, you need a different formula (segment of a circle), which this calculator does not cover.

Common Mistakes and How to Avoid Them

The most frequent error is mixing units. If you enter the diameter in inches and the height in feet, the result is meaningless. Always convert every measurement to feet first.

Another common mistake is using the diameter instead of the radius in the formula. The formula requires the radius (half the diameter). Squaring the full diameter gives a result four times too large. The calculator handles this for you, but if you are doing it by hand, remember to halve the diameter first.

A third issue is confusing cubic feet with square feet. Cubic feet is a volume (length × width × height), while square feet is an area (length × width). A cylinder with a 2 ft diameter and 3 ft height has a base area of about 3.14 ft², but a volume of 9.42 ft³.

Finally, remember that the formula assumes a perfectly uniform circular cross-section. Real tanks often have domed or dished ends, which add extra volume beyond the cylindrical section. For a rough estimate, the cylinder formula is fine; for exact capacity of a tank with curved ends, you need the manufacturer’s specification or a more complex calculation.

Limits of the Formula

The formula V = πr²h is exact only for a right circular cylinder – one where the sides are straight and the ends are flat and perpendicular to the axis. It does not apply to:

• Conical or tapered shapes – use the cone volume formula instead.
• Spheres or ellipsoids – different formulas apply.
• Cylinders with domed ends – the end caps add volume not accounted for here.
• Horizontal tanks with partial fill – the liquid surface is not a full circle, so this formula overestimates.

Also, the result is the geometric volume. For a real container, the actual usable capacity may be slightly less due to internal fittings, baffles, or sediment. For pressure vessels, the internal volume is what matters for gas storage, but the wall thickness affects the external dimensions.

Frequently Asked Questions

How do I convert cubic feet to gallons?

Multiply the volume in cubic feet by 7.48052 to get US gallons. For imperial gallons, multiply by 6.22884. The calculator’s second output does this conversion automatically using the US gallon factor.

What if I only know the radius, not the diameter?

Enter the radius doubled as the diameter, or simply use the formula V = π × r² × h directly. For example, a radius of 1 ft and height of 3 ft gives the same 9.42 ft³ as the default example.

Can I use this for a pipe that is lying horizontally?

Yes, for the total volume. The height in the formula becomes the length of the pipe. However, if you need the volume of liquid in a partially filled horizontal pipe, this formula will not work – that requires a segment area calculation based on the fill depth.

Why does the result seem too large or too small?

Check your units. A common error is entering inches as if they were feet. For example, a cylinder 12 inches in diameter and 24 inches long is 1 ft by 2 ft, giving about 1.57 ft³. If you enter 12 and 24 directly as feet, you get 2,714 ft³ – a huge overestimate. Always convert to feet first.

How many cubic feet are in a 55-gallon drum?

A 55-gallon drum holds 55 US gallons. Divide by 7.48052 to get cubic feet: 55 / 7.48052 ≈ 7.35 ft³. The drum’s actual dimensions are roughly 23 inches in diameter and 35 inches tall, which gives a similar volume when calculated.

Does the calculator work for metric measurements?

No, this calculator is designed for feet. If you have metric measurements, convert them to feet first (1 m = 3.28084 ft, 1 cm = 0.0328084 ft). Alternatively, use a metric cylinder volume calculator that outputs cubic metres or litres.

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in d | Diameter | ft | 2 | 0
in h | Height or Length | ft | 3 | 0
out vol | Volume | ft³ | pi * (d/2)^2 * h | 2
out gal | Volume (US gallons) | gal | (pi * (d/2)^2 * h) * 7.48052 | 2