To find cylinder volume, measure the inside diameter and the height, halve the diameter to get the radius r, then use V = pi x r x r x h. Keep every measurement in the same unit. For example, a tank 4 ft across and 6 ft tall holds about 75.4 cubic feet, or roughly 564 US gallons.
This guide is about geometric cylinders: cans, drums, water tanks, pipes, jars and round containers. (If you came here for engine displacement, the same formula applies to each bore, but that topic needs its own article.) First you will see the formula, then how to take the two measurements with a tape or calipers, and finally how to turn the answer into gallons or liters.
In practice, the whole job comes down to two numbers. Once you have a reliable diameter and a reliable height, the math takes less than a minute, and the converter below handles the unit changes for you.
In short: measure across the inside of the circle, measure the inside height, keep both in the same unit, and multiply pi by the radius squared by the height. Therefore, everything else on this page helps you get those two numbers right.
The units come from the SI. For instance, the US National Institute of Standards and Technology (NIST) explains on its SI volume units page that one milliliter is simply another name for one cubic centimeter, and one liter is a cubic decimeter. As a result, a cylinder measured in centimeters gives its answer directly in milliliters.
Convert Your Cylinder Volume to Liters and Gallons
Worked out your answer in cubic centimeters? Enter it here to see liters, US gallons, quarts and fluid ounces. Because 1 cc equals exactly 1 mL, the numbers carry straight across.
Key Takeaways
- The formula is V = pi r2 h, where r is the radius and h is the height.
- With a diameter, use V = 0.7854 x d2 x h instead.
- Measure inside dimensions for capacity, outside dimensions for space taken up.
- Mixing inches and feet is the most common error, so convert first.
- 1 US gallon is exactly 231 cubic inches; 1 cubic foot is about 7.48 gallons.
- A liter equals 1,000 cubic centimeters.
- Horizontal tanks that are partly full need a segment formula, not a simple fraction.
The Cylinder Volume Formula Explained
A cylinder is a circle stretched straight up. So its volume is the area of the circle multiplied by its height. The circle’s area is pi times the radius squared, which gives the familiar formula:
V = pi x r2 x h
Here pi is about 3.14159, r is the radius (half the diameter) and h is the height or length. First, square the radius, which means multiplying it by itself. Next, multiply that by pi, and finally by the height.
Most people measure the diameter, not the radius, because it is far easier to hold a tape across the full width. In that case, you can skip the halving step. Since (d/2)2 equals d2/4, the formula becomes V = (pi / 4) x d2 x h, and pi / 4 is about 0.7854.
| What you know | Formula | Watch out for |
|---|---|---|
| Radius and height | V = pi x r x r x h | Do not square the diameter by mistake |
| Diameter and height | V = 0.7854 x d x d x h | Use the inside diameter for capacity |
| Circumference and height | r = C / (2 x pi), then V = pi x r x r x h | Measure the circumference at a level line |
Recommended Tools for Measuring Cylinder Volume
The right tool depends on the size of the cylinder. Calipers suit anything small enough to fit between the jaws, such as jars, tubes and small pipes. Similarly, a tape measure covers buckets, drums and tanks. Meanwhile, a diameter tape (often called a pi tape) wraps around a large round object and reads the diameter directly, so you never have to find the exact center.
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| Tool | Best for | Typical resolution |
|---|---|---|
| Digital caliper | Diameters up to about 6 in (150 mm) | 0.0005 in or 0.01 mm |
| Steel tape measure | Heights and diameters of buckets, drums, tanks | 1/16 in or 1 mm |
| Diameter (pi) tape | Large tanks, trees, pipes you cannot reach across | Reads diameter from the circumference |
| Ruler or yardstick | Inside depth of open containers | 1/16 in or 1 mm |
How to Measure Cylinder Volume, Step by Step
- Decide inside or outside. For how much it holds, take inside measurements. For how much space it fills, measure the outside.
- Measure the diameter at the widest point. Lay the tape across the opening and slide it until the reading is largest; that line passes through the center.
- Check it a second way. Rotate a quarter turn and measure again. If the two readings differ, average them, because the cylinder may be slightly oval.
- Measure the height. Hold the tape straight and square to the base. For a container, stop at the fill line, not the rim.
- Put both numbers in one unit. Convert feet to inches, or millimeters to centimeters, before you multiply.
- Calculate. Halve the diameter, square it, then multiply by pi and by the height.
- Convert the result. Enter cubic centimeters in the converter above, or use the conversion table below for cubic inches and cubic feet.
Cylinder Volume Worked Examples
These four examples show the method on everyday objects. Each one uses the same three moves: find the radius, square it, then multiply by pi and the height.
Cylinder volume of a soda can
Say a can measures 2.6 in across and 4.8 in tall. The radius is 1.3 in, so V = 3.14159 x 1.3 x 1.3 x 4.8 = about 25.5 cubic inches. Then multiply by 16.387 to get roughly 418 mL.
That is more than the 355 mL (12 fl oz) printed on the label. However, the gap is real, not a math error. The can tapers at the top and bottom, the base domes inward, and some headspace stays empty. In other words, outside measurements describe the space a can takes up, not what it holds.
Cylinder volume of a water tank
Next, take an upright tank with an inside diameter of 4 ft and a height of 6 ft. The radius is 2 ft, so V = 3.14159 x 2 x 2 x 6 = 75.4 cubic feet. Since one cubic foot holds about 7.4805 US gallons, the tank holds about 564 gallons, or about 2,135 liters.
Cylinder volume of a pipe
Pipes also work the same way, except the “height” is the length. For instance, a pipe with a 2 in inside diameter and 10 ft (120 in) of length holds 3.14159 x 1 x 1 x 120 = about 377 cubic inches. Next, divide by 231 to get about 1.63 US gallons, or 6.18 liters. Because nominal pipe sizes rarely match the true bore, measure the inside diameter or look it up in the pipe maker’s table.
A metric example
Finally, a small jar with a radius of 3 cm and a height of 5 cm holds 3.14159 x 3 x 3 x 5 = 141.4 cm3, which is 141.4 mL. (The older version of this page rounded this to 141.3 by using 3.14 for pi.)
Converting Cylinder Volume to Gallons and Liters
Your answer comes out in cubic units of whatever you measured with: cubic inches, cubic feet or cubic centimeters. So, to turn it into liquid capacity, multiply by one of the factors below. The gallon is defined as exactly 231 cubic inches, and the NIST SI conversion factor tables list the metric equivalents.
| From | To US gallons | To liters |
|---|---|---|
| 1 cubic inch (in3) | divide by 231 | x 0.016387 |
| 1 cubic foot (ft3) | x 7.4805 | x 28.317 |
| 1 cubic centimeter (cm3) | divide by 3,785.41 | divide by 1,000 |
| 1 cubic meter (m3) | x 264.17 | x 1,000 |
For more on cubic units, see our guide on how to calculate cubic volume. Likewise, if your object is not a neat cylinder, the guide to finding the volume of a solid covers boxes, cones, spheres and water displacement.
Partly Filled Horizontal Tanks
An upright tank is easy: liquid depth divided by total height gives the fraction that is full. A tank lying on its side, however, is different, because the width of the liquid surface changes with depth. As a result, a horizontal tank filled to one quarter of its diameter holds much less than a quarter of its capacity.
To work it out, first find the area of the liquid’s cross-section, called a circular segment. With radius r and liquid depth d, the area is A = r2 x arccos((r – d) / r) – (r – d) x sqrt(2rd – d2), with the arccos in radians. After that, multiply A by the tank’s length.
| Tank 4 ft across, 8 ft long | Liquid depth | Approximate contents |
|---|---|---|
| Quarter of the diameter | 1 ft | about 147 gal (19.6% full) |
| Half of the diameter | 2 ft | about 376 gal (50% full) |
| Three quarters of the diameter | 3 ft | about 605 gal (80.4% full) |
| Full | 4 ft | about 752 gal |
Tanks with dished or rounded ends hold a little more than this straight-cylinder figure, so treat these numbers as estimates. For an exact reading, then, use the tank maker’s gauge chart.
Cylinder Volume Do and Don’t
Do
- Measure the inside diameter for capacity.
- Check the diameter twice at right angles.
- Convert all lengths to one unit first.
- Write down each reading before you calculate.
- Use the full value of pi for big tanks.
Don’t
- Square the diameter and call it the radius.
- Mix feet and inches in one formula.
- Assume a nominal pipe size is the bore.
- Read a horizontal tank as a straight fraction.
- Forget the wall thickness on outside readings.
Honest Limits of the Cylinder Volume Formula
In theory, the formula is exact for a perfect cylinder. Real objects, however, are rarely perfect. Cans taper, drums have rolled ribs, tanks have domed ends, and plastic containers bulge when full. Also, a 1/8 in error on a 12 in diameter shifts the result by about 2%, because the diameter gets squared. Therefore, the more accurate your diameter reading, the better your answer. For objects with odd shapes, filling with a measured amount of water is often more reliable than any formula.
When to Call a Professional
Generally, for a bucket or a planter, a tape measure and this page are enough. Some jobs, however, need certified numbers. Fuel and chemical tanks, for example, are often sold with a calibrated gauge chart, and regulators or insurers may require it. Similarly, well casings, septic tanks and pressure vessels have hidden internal features you cannot measure from outside. In those cases, ask the tank maker, a licensed plumber or a tank calibration service.
Frequently Asked Questions
What is the formula for cylinder volume?
The formula is V = pi x r squared x h, where r is the radius and h is the height. With the diameter d, use V = 0.7854 x d squared x h.
Can I use the diameter instead of the radius?
Yes. Either halve the diameter first, or use 0.7854 x d squared x h. Never square the full diameter and then multiply by pi, because that gives four times the real volume.
How do I find the radius of a cylinder?
Measure the diameter straight across the widest part of the circle, then divide by 2. On a large tank, divide the circumference by 2 x pi instead.
What units does cylinder volume come out in?
It comes out in cubic versions of the unit you measured with: cubic inches, cubic feet or cubic centimeters. Convert afterward to gallons or liters.
How many gallons are in a cubic foot?
One cubic foot holds about 7.4805 US gallons, or about 28.32 liters.
How do I convert cubic inches to gallons?
Divide by 231, since one US gallon is defined as exactly 231 cubic inches.
Should I measure inside or outside the cylinder?
Measure inside for capacity, meaning how much liquid it holds. Measure outside for the space it takes up, such as when fitting it into a shelf or a crate.
Is cylinder volume the same as engine cylinder displacement?
The geometry is the same: displacement per cylinder is pi x radius squared x stroke, using the bore as the diameter. Engine displacement then multiplies that by the number of cylinders.
Does it matter if I use 3.14 for pi?
It changes the answer by only about 0.05 percent, so 3.14 is fine for everyday use. For tank gauging or lab work, use the pi key on a calculator.
Why does a horizontal tank not fill evenly?
The liquid surface is narrow near the bottom and widest at the middle. So the first quarter of depth holds less than a fifth of the tank, and the middle depth holds the most.
Bottom Line on Measuring a Cylinder
To sum up, measuring a cylinder takes two careful readings and one formula. Measure the inside diameter twice, measure the height to the fill line, keep both in one unit, and calculate pi x r x r x h. Then convert with the factors above: divide cubic inches by 231 for gallons, or divide cubic centimeters by 1,000 for liters.
Finally, remember where the simple math stops. Tapered cans, domed tank ends and partly filled horizontal tanks all need a correction or a maker’s chart. For everything else, the converter at the top of this page does the unit work for you.
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