Cylinder Volume: Formula and Calculator

This calculator finds the volume of a cylinder from its radius and height, using the same units for both measurements. Enter those two dimensions to get the cylinder’s volume in cubic units, along with its equivalent in cubic yards (cy).

Formula

The volume of a right circular cylinder is V = πr²h.

• V is volume, in cubic yards (cy) when measurements are in yards.
• r is the radius of the circular base, in yards.
• h is the cylinder’s height or length, measured perpendicular to its circular ends, in yards.
• π (pi) is approximately 3.14159265.

The radius is squared before multiplying by the height. Since yards × yards × yards equals cubic yards, the units agree with the answer. If the dimensions are given in feet or inches, convert them to yards first, or calculate in the original unit and convert the resulting cubic measure.

Worked Example

Using the calculator’s default values, the radius is 1 yard and the height is 1 yard:

1. Square the radius: 1 yd × 1 yd = 1 yd².
2. Multiply by the height: 1 yd² × 1 yd = 1 yd³.
3. Multiply by pi: V = π × 1 yd³ ≈ 3.14159265 yd³.
4. Rounded to three decimal places, the volume is 3.142 cy.

Here, “cy” means cubic yard, a unit of volume. The unrounded result is π cubic yards; 3.142 cy is the calculator’s rounded display.

How to Calculate a Cylinder’s Volume

First identify the circular base and measure its radius, from the center of the circle to its edge. Then measure the cylinder’s height: the straight distance between the circular ends. For a cylinder lying on its side, this dimension is often called its length. The direction does not matter; the measurement must be perpendicular to the circular faces.

Substitute the measurements into V = πr²h. For example, if a cylinder has a radius of 2 feet and a height of 5 feet, its volume is π × 2² × 5 = 20π, or about 62.832 cubic feet. Since 1 cubic yard equals 27 cubic feet, that is approximately 2.327 cy.

If you are given the diameter rather than the radius, divide the diameter by two before using the formula. A diameter of 4 feet means a radius of 2 feet; using 4 as the radius would make the calculated volume four times too large, because radius is squared.

Using Cubic Yards and Other Units

A cubic yard is the volume of a cube measuring 1 yard on each side. Since 1 yard is 3 feet, one cubic yard contains 3 × 3 × 3 = 27 cubic feet. Since 1 yard is 36 inches, one cubic yard is 46,656 cubic inches. In metric units, 1 cubic yard is approximately 0.7646 cubic meters, or 764.6 liters.

Keep all input dimensions in a consistent unit. If you enter a radius in feet and a height in yards without converting, the numerical result does not represent cubic yards correctly. For a result in cubic yards, express both dimensions in yards before applying the formula. Useful conversions include:

• Feet to yards: divide by 3.
• Inches to yards: divide by 36.
• Meters to yards: divide by approximately 0.9144.
• Cubic feet to cubic yards: divide by 27.

Convert lengths before cubing or multiplying. A length conversion factor applies once to each dimension, so a cubic-unit conversion uses the factor three times. For example, cubic feet to cubic yards requires division by 3³, or 27—not by 3.

When the Cylinder Formula Applies

The formula describes a right circular cylinder: a solid with a circular cross-section that stays the same size along its height, with parallel circular ends. It works for a can-shaped solid, a cylindrical tank, or a straight cylindrical space. For a hollow cylinder, it gives the volume inside the outer boundary, not the amount of material in the wall.

To find the material volume of a hollow cylinder, calculate the outer cylinder’s volume and subtract the inner cylinder’s volume. If the inner and outer radii are R and r and the shared height is h, the material volume is πh(R² − r²). Use consistent units and ensure the inner radius is smaller than the outer radius.

The formula gives geometric capacity only when the cylinder’s interior is actually cylindrical and the relevant dimensions are known. It does not automatically account for curved ends, wall thickness, internal parts, or space that cannot be filled. For an irregular or tapered container, a single radius and height may not describe its volume accurately.

Common Measurement Mistakes

• Using diameter as radius: Radius is half the diameter. Because it is squared, this mistake causes a fourfold error.
• Mixing units: Convert radius and height to the same unit before calculating.
• Confusing area with volume: πr² is the base area; multiplying by h gives volume. The area alone is in square units, not cubic units.
• Rounding too early: Keep extra digits during the calculation and round the final answer to the precision the measurement supports.
• Assuming a container’s full geometric volume is usable capacity: A lid, curved end, wall, or required empty space can reduce the practical fillable amount.

Measurements themselves are rarely exact, so a result with many decimal places does not imply the dimensions were measured to that precision. Choose a sensible rounding level based on the accuracy of the radius and height.

Frequently Asked Questions

How do you calculate the volume of a cylinder in cubic yards?
Measure the radius and height in yards, then calculate V = πr²h. If you have dimensions in feet, convert the final cubic-foot result to cubic yards by dividing by 27.

What is the formula for cylinder volume?
The formula is V = πr²h: pi times the radius squared times the height. The result is in cubic units when both dimensions use the same length unit.

Can I use the diameter instead of the radius?
Yes, but first halve the diameter: r = d/2. Equivalently, V = π(d/2)²h, or V = πd²h/4.

How many cubic feet are in a cubic yard?
There are 27 cubic feet in one cubic yard because each of the cube’s three dimensions is 3 feet: 3 × 3 × 3 = 27.

Does this formula work for a hollow cylinder?
It gives the volume within a cylinder’s boundary. To find the volume of the material in a hollow cylinder, subtract the inner cylinder’s volume from the outer cylinder’s volume.

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in r | Radius | yd | 1 | 0
in h | Height | yd | 1 | 0
out cy | Volume | cy | pi * r^2 * h | 3