How to Calculate a Cylinder's Capacity in Gallons and Cubic Feet

A cylinder’s capacity equals the area of a circle base times height (π × r² × h), or the same thing written for diameter, V = 0.7854 × D² × H. That gives you a volume. To read it as gallons, convert the volume: multiply cubic feet by 7.48 for US gallons, or divide cubic inches by 231. Quick check: a cylindrical tank 3 ft wide and 5 ft tall holds 0.7854 × 3² × 5 = 35.34 cubic feet, which is about 264 US gallons. This guide shows every step, gives four worked examples with real objects, and includes a conversion table you can keep.

The two formulas (they are the same math)

Both formulas find the same number. Pick whichever matches what you measured.

If you measured the radius (center to edge):

V = π × r² × h

If you measured the diameter (edge to edge across the middle):

V = 0.7854 × D² × H

Where does 0.7854 come from? The radius is half the diameter, so r² becomes D²/4. Since π ÷ 4 = 0.7854, you can plug the diameter in directly and skip the halving step. This is the version most tank and pipe charts use, because people measure diameter with a tape more easily than radius. Try it in a cylinder volume calculator or work it by hand with the steps below.

The two-step method: volume first, then convert

Getting capacity in gallons is always two steps. People who get it wrong usually try to jump straight to gallons and lose the units.

1. Find the raw volume in whatever units you measured (cubic inches, cubic feet, or cubic meters).
2. Convert that volume into gallons using a fixed factor.

Keep your measurements in one unit system for step one. If your diameter is in inches, your height must also be in inches, and your answer lands in cubic inches. Mixing feet and inches in the same formula is the single most common mistake, and it throws the result off by orders of magnitude.

Conversion factors you will need

From	To	Multiply by
Cubic feet (ft³)	US gallons	7.48052
Cubic feet (ft³)	UK gallons	6.229
Cubic feet (ft³)	Liters	28.3168
Cubic inches (in³)	US gallons	0.004329 (÷ 231)
Cubic inches (in³)	UK gallons	0.003605 (÷ 277.42)
Cubic meters (m³)	US gallons	264.17
Cubic meters (m³)	Liters	1,000
Cubic yards	Cubic feet	27

A US liquid gallon is defined as exactly 231 cubic inches, per NIST. A UK Imperial gallon is larger, at 277.42 cubic inches, which is why the two gallon figures never match. One oil barrel, for reference, is 42 US gallons.

Worked example 1: a vertical water tank (imperial)

A cylindrical water storage tank measures 3 ft in diameter and 5 ft tall. How many gallons does it hold when full?

Step 1, volume in cubic feet:

V = 0.7854 × D² × H
V = 0.7854 × (3 ft)² × 5 ft
V = 0.7854 × 9 × 5
V = 35.343 ft³ (rounded to 3 decimals)

Step 2, convert to gallons:

US: 35.343 × 7.48052 = 264.4 US gallons
UK: 35.343 × 6.229   = 220.2 UK gallons

Sanity check: a barrel of water weighs a lot, and 264 gallons at roughly 8.3 lb per gallon is about 2,190 lb of water. That is a heavy full tank, which fits a 3 by 5 ft drum. The numbers pass the smell test. Need the reverse direction? A cylinder tank calculator handles it instantly.

Worked example 2: a metric drum (liters, then gallons)

A rain barrel has a radius of 0.5 m and a height of 2 m.

Step 1, volume in cubic meters:

V = π × r² × h
V = 3.14159 × (0.5 m)² × 2 m
V = 3.14159 × 0.25 × 2
V = 1.5708 m³

Step 2, convert:

Liters:     1.5708 × 1,000 = 1,570.8 L
US gallons: 1,570.8 ÷ 3.785 = 415.0 US gallons

Cross-check by a second path: 1.5708 m³ is 55.47 ft³, and 55.47 × 7.48052 = 414.9 gallons. Two routes, the same answer. That is how you know the conversion held. This is also why a good volume in liters tool and a volume in gallons tool should agree to within rounding.

Worked example 3: the “55-gallon” drum (real object, verifiable)

Grab a standard steel drum. Its internal dimensions are close to 22.5 inches in diameter and 33.5 inches tall (typical industry spec for a DOT-approved 55-gallon drum).

V = 0.7854 × 22.5² × 33.5
V = 0.7854 × 506.25 × 33.5
V = 13,319.9 in³

Convert:

US gallons: 13,319.9 ÷ 231 = 57.66 US gallons
Cubic feet: 13,319.9 ÷ 1,728 = 7.71 ft³

Here is the useful surprise. The geometry says about 57.7 gallons, yet the drum is sold as a 55-gallon drum. The difference is deliberate headspace. Tanks and drums are almost never filled to the brim, because liquids expand, slosh, and need room for a bung and vapor. So the nameplate capacity is a safe working fill, not the geometric maximum. Whenever a container’s rated capacity looks smaller than your math, headspace is usually why.

Worked example 4 (advanced): a horizontal tank that is only part full

Most guides stop at full vertical tanks. Real tanks often lie on their side and sit half empty, and the simple formula no longer works, because a horizontal cylinder does not fill in even proportions. At the bottom, a small rise in depth covers only a narrow strip of liquid.

For a horizontal cylinder filled to depth h, first find the liquid’s cross-section area:

A = r² × arccos((r − h) / r) − (r − h) × √(2rh − h²)

Then multiply by the tank length L to get the volume.

Take a tank with radius 2 ft, length 6 ft, filled 1 ft deep:

arccos((2 − 1) / 2) = arccos(0.5) = 1.0472 radians
A = 2² × 1.0472 − (2 − 1) × √(2 × 2 × 1 − 1²)
A = 4 × 1.0472 − 1 × √3
A = 4.1888 − 1.7320 = 2.4568 ft²

Volume = 2.4568 × 6 = 14.74 ft³
US gallons = 14.74 × 7.48052 = 110.3 US gallons

Notice the payoff. The tank is filled to 1 ft on a 4 ft diameter, so it is a quarter of the way up by depth, yet it holds only about 19.6 percent of its full volume. That gap is exactly why a dipstick reading on a horizontal tank is never a straight percentage. A dedicated horizontal cylinder calculator does this segment math for you.

US gallons vs UK gallons: do not mix them up

A US gallon is 231 cubic inches. A UK Imperial gallon is 277.42 cubic inches, about 20 percent larger. So the same tank holds fewer UK gallons than US gallons. If a spec sheet lists gallons without saying which, check the country of origin before you trust the number. This one detail causes constant confusion in tank sizing and fuel figures.

Common mistakes to avoid

• Using diameter as radius. If you measure across the whole circle, that is diameter. Either halve it, or use the 0.7854 diameter formula. Doubling this value quadruples your answer.
• Mixing units mid-formula. Feet with inches, or centimeters with meters, wrecks the result. Convert to one unit first.
• Filling to 100 percent. Geometric volume is the ceiling, not the real capacity. Leave headspace for working fills.
• Assuming horizontal tanks fill evenly. They do not. Use the segment formula for partial fills.
• Forgetting which gallon. US and UK gallons differ by roughly 20 percent.

Frequently asked questions

How do I find gallons in a cylinder from cubic feet? Multiply the cubic feet by 7.48052 for US gallons, or by 6.229 for UK gallons.

What is the formula for cylinder capacity in gallons? Find the volume with V = 0.7854 × D² × H, then convert. In cubic feet, multiply by 7.48 for US gallons. In cubic inches, divide by 231.

How many gallons is a cubic foot of water? One cubic foot holds 7.48 US gallons, which is about 62.4 lb of water at room temperature. A quick way to estimate any tank is to find its cubic feet, then multiply by 7.5 in your head for a close US-gallon figure.

How do I convert cubic inches to gallons? Divide cubic inches by 231 for US gallons, or by 277.42 for UK gallons. So a 13,320 in³ drum is 13,320 ÷ 231 = 57.7 US gallons.

Why does my “55-gallon” drum calculate to almost 58 gallons? The extra volume is intentional headspace. The geometric capacity is near 57.7 gallons, but the drum is rated at 55 to leave room for expansion, vapor, and a safe fill line. Rated capacity is usually below the mathematical maximum for exactly this reason.

How do I calculate gallons in a horizontal cylinder tank that is half full? You cannot just take half the full volume unless it is filled to the exact center line. For any other depth, use the circular-segment area formula, A = r² × arccos((r − h)/r) − (r − h) × √(2rh − h²), then multiply by the tank length and convert to gallons. A partial fill below center holds less than the proportional amount, and above center it holds more.

Do I use the same formula for metric tanks? Yes. The formula is identical. Measure in meters, get cubic meters, then multiply by 264.17 for US gallons or by 1,000 for liters.

Sources and verification

The US gallon is defined as 231 cubic inches and the UK Imperial gallon as 277.42 cubic inches, per NIST unit references. Cylinder volume formulas follow the standard geometry described at Wolfram MathWorld. Standard 55-gallon drum internal dimensions are industry-typical for DOT-approved steel drums. Every calculation in this article was worked step by step and independently checked.

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Author: CylinderVolume-Calculator.com Editorial Team
Published: 7 August 2026
Last reviewed: 7 August 2026
Fact-checked by: CVC Editorial Team

This article was drafted with AI assistance and reviewed for accuracy before publishing. All calculations independently verified.