Cubic Feet Calculator Circle: Volume of a Cylinder

This calculator works out the volume of a cylinder in cubic feet from its diameter and height. You enter the circle’s diameter and the cylinder’s height in feet, and you get back the volume in cubic feet. This is the standard way to measure round containers, pipes, wells, and tanks when you need the answer in imperial units.

Formula

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

V = π × r² × h

Where:

• V = volume in cubic feet (cu ft)
• Ï€ ≈ 3.14159
• r = radius of the circle in feet (half the diameter)
• h = height (or length) of the cylinder in feet

If you only have the diameter (d), replace r with d/2: V = π × (d/2)² × h. This is the exact formula used in the calculator above.

Worked Example

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

1. Find the radius: r = d/2 = 2/2 = 1 ft
2. Square the radius: r² = 1² = 1 sq ft
3. Multiply by Ï€: 1 × Ï€ = 3.14159 sq ft (this is the circle’s area)
4. Multiply by height: 3.14159 × 3 = 9.42477 cu ft

Rounded to two decimals, the volume is 9.42 cubic feet. The calculator’s first output shows exactly that. The second output, circle area = 3.14 sq ft, is the intermediate step.

When to Use This Calculation

You need this whenever a round container’s capacity is asked for in cubic feet. Common real-world cases:

• Concrete for a round footing, pier, or column
• Soil or compost for a round planter or raised bed
• Water volume in a round tank, well, or pool (1 cu ft = 7.48052 US gallons)
• Air volume in a round duct or pipe
• Grain or sand in a cylindrical silo

If the container is not a perfect cylinder—for example, a cone-shaped pile or a sphere—this formula does not apply. A cone uses V = (1/3)πr²h; a sphere uses V = (4/3)πr³.

How to Read the Result

The result is a volume, not an area. One cubic foot is a cube 1 foot on each side. To convert to other units:

• 1 cubic foot = 1,728 cubic inches
• 1 cubic foot = 7.48052 US gallons
• 1 cubic foot = 28.3168 liters
• 1 cubic foot = 0.0283168 cubic meters

For example, a 2-ft diameter, 3-ft tall cylinder holds 9.42 cu ft, which is about 70.5 US gallons. If you are ordering concrete, note that ready-mix is usually sold by the cubic yard (27 cu ft), so 9.42 cu ft would be 0.35 cubic yards.

Common Mistakes and Unit Mix-Ups

The most frequent error is mixing units. If you measure diameter in inches but height in feet, the formula gives nonsense. Convert everything to feet first: divide inches by 12. For instance, a 6-inch diameter pipe is 0.5 ft.

Another mistake is using the diameter instead of the radius in the formula. The formula requires r², not d². Using d² gives a result four times too large. The calculator above handles this by dividing the diameter by 2 internally, but if you do it by hand, do not forget that step.

Rounding too early also causes errors. If you round π to 3.14 and the radius to one decimal, you can be off by several percent on large volumes. Keep full precision until the final step.

Limits of the Formula

This formula assumes a perfectly straight cylinder with a uniform circular cross-section. Real objects deviate:

• Tanks with domed or dished ends hold more than a straight cylinder
• Pipes with wall thickness have a smaller internal volume than the outer dimensions suggest
• Silos with tapered bottoms are not full cylinders

For such shapes, you need additional formulas or a numerical approximation. Also, if the cylinder is partially filled, the volume is not simply πr²h; you need the segment area of a circle, which involves trigonometry.

Practical Tips for Measuring

To get an accurate result:

1. Measure the inside diameter if you need internal volume (e.g., water capacity). For concrete, use the outer dimensions.
2. Take the diameter at several points and average them—round objects are rarely perfectly round.
3. Measure height from the bottom to the top of the fill line, not the total container height if you only need partial volume.
4. If the object is horizontal (like a pipe lying on its side), the volume calculation is different—you need the area of a circular segment times the length.

For a horizontal cylinder, the formula is more complex: V = L × (r² × arccos((r-h)/r) – (r-h) × sqrt(2rh – h²)), where h is the liquid depth. That is beyond this simple calculator.

Frequently Asked Questions

How do I calculate cubic feet of a circle? A circle alone has no volume—it is a flat shape. You need a cylinder (circle plus height). Use V = π × (d/2)² × h, with all measurements in feet. The result is cubic feet.

What is the volume of a 2-foot diameter circle? A 2-ft diameter circle has an area of π × (1)² = 3.14 sq ft. Its volume depends on height. If the height is 1 ft, the volume is 3.14 cu ft; if 3 ft, it is 9.42 cu ft.

How many cubic feet in a 55-gallon drum? A 55-gallon drum holds 55 US gallons. Since 1 cu ft = 7.48052 gallons, 55 / 7.48052 = 7.35 cu ft. The drum’s dimensions (about 23 in diameter, 35 in height) give approximately that volume when calculated with this formula.

Can I use this for a round pool? Yes, if the pool has a uniform depth and a circular shape. Measure the diameter at the water line and the average depth, then use the formula. For a pool with a sloped bottom, divide it into sections or use an average depth.

What is the difference between cubic feet and square feet? Square feet measure area (2D), cubic feet measure volume (3D). A circle has square feet of area, but only a cylinder has cubic feet of volume. You cannot convert directly between them without knowing the height.

How do I convert cubic feet to gallons? Multiply cubic feet by 7.48052 to get US gallons. For imperial gallons, multiply by 6.22884. For example, 9.42 cu ft × 7.48052 = 70.5 US gallons.

Related

• Area Calculator Square Meters: How to Measure
• Area Calculator Sq Feet: Formula & How to Use
• Area Calculator in Square Feet: How It Works

in d | Circle diameter | ft | 2 | 0
in h | Height | ft | 3 | 0
out vol | Volume | cu ft | pi * (d/2)^2 * h | 2
out area | Circle area | sq ft | pi * (d/2)^2 | 2