Cylinder Gallons: Formula and Calculator

Calculate a cylinder’s liquid capacity in gallons by entering its inside diameter and height; this calculator converts the cylinder’s volume to US gallons. Use the same length unit for both measurements, and measure the space inside the cylinder rather than its outside dimensions.

Formula

A cylinder’s volume is the area of its circular base multiplied by its height. In symbols, V = πr²h, where V is volume in cubic units, r is the inside radius, and h is the inside height, measured in the same unit. Since the calculator asks for diameter d, use r = d / 2.

To convert cubic inches to US liquid gallons, divide by 231: gallons = π(d / 2)²h / 231. The value 231 is the number of cubic inches in one US liquid gallon. The calculator’s first result is US gallons; its second is the cylinder volume in cubic inches.

Worked Example

Using the calculator’s defaults—an inside diameter of 12 inches and an inside height of 24 inches:

1. Radius: 12 ÷ 2 = 6 inches.
2. Volume: π × 6² × 24 = 864π ≈ 2,714.34 cubic inches.
3. Capacity: 2,714.34 ÷ 231 ≈ 11.75 US gallons.

The calculator rounds the capacity to two decimal places, so it displays 11.75 US gallons. The volume result is 2,714.34 cubic inches.

When to Use the Calculation

This calculation applies when a container has a circular cross-section and straight, parallel sides, such as a simple vertical tank or open cylindrical vessel. It gives the volume of the space inside the cylinder. It does not automatically account for liquid already in the container, a rounded or sloped bottom, internal fittings, or a lid that takes up space.

For a partly filled upright cylinder with a flat bottom, use the liquid depth in place of the full height to calculate the liquid volume. For a horizontal cylinder, the liquid depth does not represent the length of a full circular slice: the cross-section is only partly filled, so the full-cylinder formula alone is insufficient.

Choosing Measurements and Units

Measure the inside diameter across the widest part of the circular interior, and measure the inside height from the interior bottom to the top of the usable space. If you only know the inside radius, double it to get the diameter for this calculator. If you only have outside measurements, subtract the wall thickness from each side where appropriate; otherwise, the calculated capacity will be too large.

This calculator takes inches and returns US liquid gallons. Keep diameter and height in inches; mixing inches and feet without conversion produces an incorrect result. For metric measurements, first use consistent units: with diameter and height in centimeters, the volume is in cubic centimeters, and 1,000 cubic centimeters equal 1 liter. One US liquid gallon is approximately 3.785 liters. A US gallon is not the same as an Imperial gallon, which is approximately 4.546 liters.

• To convert inches to centimeters, multiply by 2.54.
• To convert feet to inches, multiply by 12.
• To convert US gallons to liters, multiply by approximately 3.785.

Reading the Result and Avoiding Errors

The result is the cylinder’s theoretical internal capacity when filled to the measured height. Actual usable volume may be lower if the vessel must not be filled to its rim, has a non-flat base, or contains objects or components inside. For a practical fill amount, measure the actual interior geometry and leave any required headspace rather than treating the mathematical capacity as a fill recommendation.

• Do not use the diameter as the radius. The radius is half the diameter, and squaring it makes this mistake especially significant.
• Use inside dimensions. Outside diameter includes the wall and overstates capacity.
• Keep units consistent. The diameter and height must be in the same unit before applying the formula.
• Round only at the end. Rounding the radius or volume early can alter the final gallon figure, particularly for small containers.

Limits of the Cylinder Model

The formula assumes a perfect circular cross-section and a constant diameter along the full height. It will not give an exact result for a tapered bucket, a tank with domed ends, a cylinder with a curved bottom, or a container whose sides bulge or narrow. For those shapes, divide the interior into simpler sections and calculate each section separately, or use measured manufacturer capacity when available.

It also calculates volume, not mass or weight. How much a gallon of a particular liquid weighs depends on the liquid and its conditions; gallons alone do not determine weight. Likewise, a capacity estimate does not indicate whether a container is structurally suitable for holding a liquid.

Frequently Asked Questions

How do you calculate gallons in a cylinder?
Calculate the cylinder’s volume with π × radius² × height, using consistent length units. For measurements in inches, divide the cubic-inch result by 231 to get US liquid gallons.

How many gallons are in a cylinder 12 inches wide and 24 inches tall?
If those are the inside diameter and height, its theoretical capacity is about 11.75 US gallons.

Can I use feet instead of inches?
Yes, provided both measurements use feet and you convert the resulting cubic feet to gallons. One cubic foot is 7.48052 US gallons, so multiply the volume in cubic feet by that factor. Alternatively, convert feet to inches first and use the calculator.

Does this formula work for a horizontal cylinder?
It gives the cylinder’s total capacity if you use its full internal length as the cylinder height and its inside diameter. It does not directly give the amount of liquid in a partially filled horizontal cylinder.

Is a US gallon the same as an Imperial gallon?
No. A US liquid gallon is about 3.785 liters, while an Imperial gallon is about 4.546 liters. This calculator reports US liquid gallons.

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in d | Inside diameter | in | 12 | 0
in h | Inside height | in | 24 | 0
out gal | Capacity | US gal | pi * (d / 2)^2 * h / 231 | 2
out vol | Volume | in³ | pi * (d / 2)^2 * h | 2