Cubic Feet Calculator Cylinder Formula

This calculator works out the volume of a cylinder in cubic feet using the standard formula V = π × r² × h. You enter the radius (or diameter) and height in feet, inches, or a mix of both, and it returns the volume in cubic feet, plus the volume in gallons and liters as a bonus. The result is the space inside the cylinder, useful for tanks, pipes, silos, and other cylindrical containers.

Formula

The volume of a cylinder is the area of its circular base multiplied by its height. In words: cubic feet = π × (radius in feet)² × (height in feet).

In symbols:

V = π r² h

• V = volume in cubic feet (ft³)
• Ï€ ≈ 3.14159265 (pi, a constant)
• r = radius of the circular base in feet (half the diameter)
• h = height (or length) of the cylinder in feet

If you measure the diameter instead, use r = d/2. If you measure in inches, convert to feet first by dividing by 12, because the formula requires consistent units.

Worked Example

Using the default values from the calculator: radius = 2 ft, height = 5 ft.

1. Square the radius: r² = 2² = 4
2. Multiply by π: 4 × π ≈ 12.56637
3. Multiply by height: 12.56637 × 5 = 62.83185
4. Round to two decimals: 62.83 cubic feet

The calculator shows 62.83 cu ft. For gallons, multiply by 7.48052 (since 1 cubic foot ≈ 7.48052 US gallons): 62.83 × 7.48052 ≈ 470.0 gallons. For liters, multiply by 28.3168: 62.83 × 28.3168 ≈ 1779 liters. These match the outputs.

When to Use This Formula

Use the cylinder volume formula any time you need the capacity of a cylindrical container or the volume of a cylindrical space. Common real-world applications include:

• Water tank capacity (residential, agricultural, or fire suppression)
• Fuel or chemical storage tanks
• Pipe volume (for flow rate or filling time)
• Concrete volume for cylindrical footings or columns
• Compressed gas cylinder contents
• Grain silo or storage bin volume

The formula works for any cylinder—vertical or horizontal—because volume is independent of orientation. For a horizontal tank, the same formula gives the total volume, but if you need the volume at a partial fill level, you need a different calculation involving the segment of a circle.

How to Measure Radius and Height

For a vertical cylinder, measure the inside diameter at the widest point (or the outside diameter if wall thickness is negligible). Divide by 2 to get the radius. Measure the height from the bottom to the top, again using inside dimensions for capacity.

If the cylinder has domed or dished ends (like many pressure tanks), the simple cylinder formula only covers the straight section. You must add the volume of the end caps separately, which requires a different formula depending on the shape (hemispherical, elliptical, etc.).

When measuring a pipe, the height is actually the length of the pipe. For a pipe with an internal diameter of 4 inches (radius 2 inches) and a length of 10 feet, convert the radius to feet: 2 in ÷ 12 = 0.1667 ft. Then V = π × (0.1667)² × 10 ≈ 0.8727 cu ft.

Common Mistakes and Unit Mix-Ups

The most frequent error is mixing units without conversion. If you enter the radius in inches and the height in feet, you get a nonsense result. Always convert all measurements to feet before using the formula.

• Inches to feet: divide by 12
• Yards to feet: multiply by 3
• Centimeters to feet: divide by 30.48
• Meters to feet: multiply by 3.28084

Another common mistake is using the diameter instead of the radius. The formula uses r², so if you accidentally plug in the diameter, your volume will be four times larger than correct. For example, a cylinder with diameter 4 ft and height 5 ft has radius 2 ft, so volume is π × 2² × 5 = 62.83 cu ft, not π × 4² × 5 = 251.33 cu ft.

Rounding too early can also cause errors. Keep at least four decimal places during intermediate steps, then round the final answer. For instance, using π ≈ 3.14 instead of 3.14159 on a large tank can change the result by several cubic feet.

Limits of the Formula

The formula V = πr²h assumes a perfect right circular cylinder with uniform cross-section and flat ends. Real objects deviate:

• Wall thickness: For a tank, use inside dimensions for capacity. Outside dimensions give the total volume including the wall material.
• Elliptical or irregular cross-sections: The formula won’t work; you need the area of the actual cross-section.
• Tapered cylinders (cones): Use the cone volume formula instead.
• Domed or dished ends: Add the end cap volume separately.
• Thermal expansion: Liquids expand with temperature; the cylinder volume is fixed, but the liquid volume changes. For precise storage, account for the liquid’s coefficient of expansion.

Also note that the formula gives the total volume, not the usable volume. Tanks often have a maximum fill level below the top for safety or expansion, so the actual usable capacity may be less.

Converting to Other Units

Once you have cubic feet, you can convert to other common units:

• US gallons: multiply by 7.48052
• Imperial gallons: multiply by 6.22884 (British)
• Liters: multiply by 28.3168
• Cubic inches: multiply by 1728 (since 1 ft³ = 12³ in³)
• Cubic yards: divide by 27
• Pounds of water: multiply by 62.428 (at 39.2°F, water density)

For example, the default cylinder (62.83 cu ft) holds about 470 US gallons. A typical 55-gallon drum has a volume of about 7.35 cubic feet (55 ÷ 7.48052).

Frequently Asked Questions

How do I find cubic feet of a cylinder if I only have the diameter?

Divide the diameter by 2 to get the radius, then use the same formula. For example, a cylinder with diameter 4 ft and height 6 ft has radius 2 ft, so volume = π × 2² × 6 = 75.40 cu ft.

Can I use this formula for a horizontal cylinder?

Yes, the total volume is the same regardless of orientation. But if you need the volume at a partial fill (like a fuel tank lying on its side), you need a more complex formula involving the circular segment area. This calculator only gives the full volume.

What is the formula for a cylinder in cubic inches?

Use the same formula but with radius and height in inches: V = π × r² × h, and the result is in cubic inches. To convert to cubic feet, divide by 1728.

How many gallons does a 2 ft × 5 ft cylinder hold?

Using the default example, the volume is 62.83 cubic feet. Multiply by 7.48052 to get approximately 470 US gallons. That’s the total capacity if filled to the very top.

Does the formula work for a pipe?

Yes, a pipe is just a long cylinder. Measure the internal radius and the length (height) in feet, then apply V = πr²h. For a 2-inch diameter pipe (radius 1 inch = 0.0833 ft) that is 10 feet long, the volume is about 0.218 cubic feet, or about 1.63 gallons.

What if my cylinder has curved ends?

The simple formula only covers the straight cylindrical section. For a tank with hemispherical or elliptical heads, you need to add the volume of those end caps. For hemispherical ends, each cap has volume (2/3)πr³, so add two of those to the cylinder volume.

Related

• Biplane EF Calculator: Ejection Fraction by Echo
• Bing Fraction Calculator: How to Use It
• Binary Fraction Calculator: Convert & Add

in r | Radius | ft | 2 | 0
in h | Height | ft | 5 | 0
out vol | Volume | cu ft | pi * r^2 * h | 2
out gal | US gallons | gal | vol * 7.48052 | 1
out l | Liters | L | vol * 28.3168 | 0