Cylinder Volume Calculator

Using the calculator is straightforward. You just need two measurements: the radius (or diameter) of the circular base and the height of the cylinder. Enter those values, select your unit of measurement, and the calculator spits out the volume instantly.

• Radius: The distance from the center of the circle to its edge.
• Diameter: If you measured across the full circle instead, enter that in the diameter field. The calculator will handle the conversion.
• Height: The straight-line distance from the bottom base to the top base.

Make sure your radius (or diameter) and height are in the same unit before entering them. Mixing inches and centimeters, for example, will give you a meaningless result. Once you hit calculate, you can usually convert the output to a different unit right on the same screen.

Calculating cylinder volume comes down to a simple concept: find the area of the circular base, then multiply it by the height. That's it. The circle's area tells you how much space is covered at one cross-section, and the height tells you how far that cross-section extends.

The result is expressed in cubic units. So if your measurements are in inches, the volume comes out in cubic inches. If you're working in centimeters, you get cubic centimeters (also written as cm³ or milliliters when dealing with liquids).

Most everyday calculations only require a few seconds once you know which values to plug in. The trickier part is usually making sure you're measuring the right thing — radius versus diameter trips people up more often than the math itself does.

The standard formula for cylinder volume is built on the area of a circle. There are two versions depending on whether you measured the radius or the diameter. Both give the same result; it just depends on what measurement you have on hand.

A hollow cylinder (sometimes called a cylindrical shell or annular cylinder) has a tube-like shape with empty space running through the middle. Think of a pipe, a cardboard toilet paper roll, or a section of PVC tubing. To find how much material fills the walls of that shape, or how much fluid it can carry in its hollow core, you need a slightly different approach.

The calculator for a hollow cylinder asks for three inputs: the outer radius, the inner radius, and the height. With those three values, it calculates the volume of just the solid portion of the walls, not the empty space inside.

An oblique cylinder is one where the sides lean at an angle instead of standing perfectly vertical. Picture a can that's been tilted or a stack of coins that's been pushed sideways. It looks more complicated, but the volume formula is actually identical to that of a right (straight) cylinder.

V = π × r² × h

The key is using the perpendicular height, not the slant height. The perpendicular height is the straight vertical distance between the two circular bases, measured at a right angle to the base. If you accidentally use the longer slant-side measurement instead, you'll overestimate the volume.

This is a consequence of Cavalieri's principle, which says that if two solids have the same cross-sectional area at every level and the same height, they have the same volume regardless of how the shape leans. So don't overthink the tilt. Just get the true vertical height and use the standard formula.

Once you've calculated a volume, you might need it in a different unit. Here are the most common conversions you'll run into:

For liquid-capacity problems, converting to liters or gallons usually makes the result more intuitive. For construction or material volume, sticking with cubic feet or cubic meters tends to be more practical. Most online calculators offer a unit dropdown so you can skip the conversion math entirely.

Sometimes seeing the work done out in full is more useful than just reading a formula. Here are a few examples covering different scenarios.

Example 1: Water tank (radius given)
A cylindrical water tank has a radius of 3 feet and a height of 8 feet.
V = π × 3² × 8 = π × 9 × 8 = 72π ≈ 226.19 cubic feet

Example 2: Soup can (diameter given)
A can has a diameter of 7.4 cm and a height of 11.2 cm.
Radius = 7.4 / 2 = 3.7 cm
V = π × 3.7² × 11.2 = π × 13.69 × 11.2 ≈ 481.87 cm³

Example 3: Pipe wall material (hollow cylinder)
A steel pipe has an outer diameter of 10 cm, inner diameter of 8 cm, and length of 50 cm.
Outer radius = 5 cm, Inner radius = 4 cm
V = π × (5² − 4²) × 50 = π × (25 − 16) × 50 = π × 9 × 50 ≈ 1,413.72 cm³

Working through examples like these helps you catch errors before they matter. If an answer seems wildly off, double-check whether you squared the radius (not the diameter) and whether you used the right height.

Understanding how these four values relate to each other helps you think about cylinders more intuitively, not just plug numbers into a formula.

Radius and diameter are directly linked: diameter is always twice the radius. Simple enough. But because the radius gets squared in the volume formula, doubling the radius doesn't double the volume. It quadruples it. A cylinder with a radius of 4 cm holds four times the volume of one with a radius of 2 cm (assuming the same height). That's easy to underestimate.

Height has a straightforward linear relationship with volume. Double the height, double the volume. No squaring involved. So if you're trying to maximize capacity, increasing the radius has a much bigger payoff than increasing the height by the same amount.

This relationship matters in practical design. A wider, shorter cylinder holds more than a tall, narrow one with the same total surface area. Engineers and designers account for this all the time when sizing tanks, containers, and pipes.

Cylinder volume calculations show up in more places than most people realize.

• Plumbing and piping: Estimating flow capacity and the amount of material needed to manufacture pipe sections.
• Water and fuel storage: Sizing tanks for homes, farms, and industrial facilities.
• Cooking and food packaging: Determining fill volumes for cans, jars, and cylindrical molds.
• Construction: Calculating how much concrete is needed to fill cylindrical columns or posts.
• Engine design: Engine displacement is based on the combined volume of all cylinders in the engine block.
• HVAC and ventilation: Sizing cylindrical ductwork for proper airflow.
• Manufacturing: Calculating material volume for cylindrical parts to estimate weight and cost.

Even something as simple as figuring out how much soil to pour into a round planter or how much paint a cylindrical column needs involves this calculation. It's a surprisingly practical skill once you start noticing cylinders everywhere.

A few errors come up over and over, especially for people who don't do this calculation regularly.

• Using diameter instead of radius: This is the most frequent mistake. The formula uses radius. If you plug in the diameter without dividing by 2 first, your volume will be off by a factor of 4.
• Forgetting to square the radius: V = π × r² × h, not π × r × h. Skipping the square is a quick way to get a completely wrong answer.
• Mixing units: Measuring the radius in inches and the height in feet without converting leads to nonsense results. Pick one unit and stick with it throughout.
• Using slant height on an oblique cylinder: Always use the perpendicular height, the true vertical distance between the bases.
• Confusing inner and outer radius on hollow cylinders: Using the wrong one changes the answer significantly, especially when wall thickness is a large portion of the overall size.
• Rounding π too early: Using 3.14 instead of 3.14159 (or your calculator's π key) introduces rounding error that compounds in larger calculations. Let the calculator handle π until the very last step.

Most of these are easy to avoid once you're aware of them. When in doubt, write out each step rather than trying to do it all in your head.