Cylinder Gallon Calculator: Volume in Gallons

This calculator works out the volume of a cylinder in US gallons from its diameter (or radius) and height. You enter the cylinder’s dimensions in inches, feet, or centimeters, and it returns the capacity in gallons, along with the volume in cubic inches and liters. The result is the total liquid volume the cylinder can hold when filled to the brim.

Formula

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

V = π × r² × h

Where:

• V = volume in cubic inches (in³)
• Ï€ ≈ 3.14159
• r = radius of the cylinder = half the diameter (in)
• h = height of the cylinder (in)

To convert cubic inches to US gallons, divide by 231 (since 1 US gallon = 231 in³). If you measure in feet, first convert to inches (1 ft = 12 in) or use the direct factor: 1 ft³ = 7.48052 US gallons.

Worked Example

Using the default values: diameter = 12 in, height = 24 in.

1. Find the radius: r = d/2 = 12/2 = 6 in
2. Compute the base area: A = π × r² = 3.14159 × 6² = 3.14159 × 36 = 113.097 in²
3. Multiply by height: V = 113.097 × 24 = 2714.34 in³
4. Convert to gallons: V = 2714.34 / 231 = 11.75 US gal

The calculator shows 11.75 gallons, matching the step-by-step result.

When to Use This Calculator

You need this calculator whenever you have a cylindrical container and want to know its liquid capacity in gallons. Common situations:

• Aquarium sizing – a cylindrical fish tank or filter chamber
• Fuel or water storage – tanks, barrels, drums
• Propane or compressed gas cylinders (though those are often rated in pounds or cubic feet)
• DIY projects – making a rain barrel, a planter, or a fermentation vessel
• Shipping – estimating how much liquid fits in a cylindrical drum

For a partially filled cylinder, the calculator only gives the full volume. If you need the volume at a certain fill height, that requires a different formula (the segment of a circle area times height).

How to Measure a Cylinder Correctly

Accurate measurements are the difference between a useful estimate and a real error. Follow these steps:

1. Measure the inside diameter – not the outside – for true capacity. The wall thickness reduces the interior volume.
2. If the cylinder has flat ends, measure from the inside bottom to the inside top. For domed or dished ends, the formula changes – this calculator assumes flat ends.
3. Use a rigid tape measure or calipers for small cylinders. For large tanks, measure in several places and average.
4. Convert all measurements to the same unit before calculating. If you mix inches and feet, the result will be wrong.

For a horizontal cylinder (lying on its side), the same formula applies only when it is full. If you need the volume at a partial fill in a horizontal tank, you need a more complex calculation involving the segment area.

Common Mistakes and Misconceptions

The most frequent error is mixing up US gallons and imperial gallons. 1 US gallon = 231 in³, while 1 imperial gallon = 277.42 in³. This calculator uses US gallons. If you need imperial gallons, multiply the US result by 0.83267.

Another common mistake is using the diameter instead of the radius in the formula. Remember: r = d/2. Squaring the diameter directly gives a result 4 times too large.

A third issue is forgetting to convert units. If you measure in feet, the volume comes out in cubic feet. To get gallons, multiply cubic feet by 7.48052 (US). If you measure in centimeters, the volume is in cubic centimeters; divide by 3785.41 to get US gallons.

Finally, this calculator assumes a perfectly straight cylinder with flat ends. Real tanks often have rounded or conical ends, which add or subtract volume. For those, you need a tank-specific formula.

Units and Conversions

Here are the key conversion factors you might need:

• 1 US gallon = 231 cubic inches
• 1 US gallon = 0.133681 cubic feet
• 1 US gallon = 3.78541 liters
• 1 imperial gallon = 277.42 cubic inches
• 1 liter = 61.0237 cubic inches

If you measure in metric, the simplest path is to compute the volume in cubic centimeters (cm³) and divide by 3785.41 to get US gallons. For example, a cylinder with a 30 cm diameter and 50 cm height:

r = 15 cm, V = π × 15² × 50 = 35,343 cm³, gallons = 35,343 / 3785.41 = 9.34 US gal.

Limitations of the Formula

The formula V = πr²h is exact only for a right circular cylinder with flat, perpendicular ends. Real-world deviations:

• Domed or dished heads – common on pressure vessels and some tanks – add or subtract volume. The formula does not account for them.
• Tapered cylinders (like a bucket) are actually frustums, not cylinders. Use the frustum formula instead.
• Wall thickness – if you measure outside dimensions, the interior volume is smaller. For thin-walled containers the error is small, but for thick-walled ones it matters.
• Thermal expansion – liquids expand when heated. A cylinder filled to the brim at 20°C may overflow at 30°C. Leave headspace for safety.

For most household and workshop uses, the error from these factors is under a few percent. For industrial or safety-critical applications, consult engineering standards.

Frequently Asked Questions

How many gallons is a 12-inch by 24-inch cylinder?

Using the calculator’s defaults: a cylinder with a 12-inch diameter and 24-inch height holds 11.75 US gallons. That’s about 44.5 liters.

Does this work for a horizontal cylinder?

Yes, but only when the cylinder is completely full. For a partially filled horizontal cylinder, the volume depends on the fill height and requires a different formula involving the circular segment area. This calculator gives the total capacity, not partial fill.

What is the difference between US gallons and imperial gallons?

US gallons are smaller: 1 US gallon = 231 in³, while 1 imperial gallon = 277.42 in³. So an imperial gallon is about 1.2 times larger. This calculator returns US gallons. To convert to imperial, multiply the result by 0.83267.

Can I use this for a propane tank?

You can calculate the water capacity of a propane cylinder, but propane tanks are typically filled to only 80% capacity for safety. Also, many propane tanks have domed ends, so the flat-end formula will overestimate. Check the tank’s stamped water capacity for the official number.

How do I convert the result to liters?

Multiply the US gallons by 3.78541. For example, 11.75 gallons × 3.78541 = 44.48 liters. The calculator already shows liters in the second output.

What if my cylinder has a different shape?

If the container is not a right circular cylinder with flat ends, this formula is not accurate. For a tapered container (frustum), use V = (1/3)πh(r1² + r1r2 + r2²). For a sphere, use V = (4/3)πr³. For irregular shapes, use water displacement.

Related

• Arc Length of Vector Calculator: Formula & Steps
• Arc Length to Straight Line Calculator
• Arc Length to Radius Calculator: Formula & Steps

in d | Diameter | in | 12 | 0
in h | Height | in | 24 | 0
out gallons | Volume | US gal | (pi * (d/2)^2 * h) / 231 | 2
out liters | Volume | L | pi * (d/2)^2 * h * 0.0163871 | 2
out cu_in | Volume | in³ | pi * (d/2)^2 * h | 1