The Formula for Cylinder Volume

The volume of a cylinder is π × r² × h, where r is the radius of the circular base and h is the height of the cylinder. You multiply the area of the circular base by how tall the cylinder is. That's it—three numbers, one multiplication.

The radius is half the width across the circle. If you measure the full width (the diameter), divide it by 2 to get the radius. The height is how tall the cylinder stands, measured straight up from the base to the top.

The symbol π (pi) is approximately 3.14159. Most calculators have a π button so you don't have to type it out. If yours doesn't, using 3.14 is close enough for most purposes.

Key Takeaways

  • The volume formula is π × r² × h, where r is the radius (half the diameter) and h is the height.
  • Square the radius first (multiply it by itself), then multiply by π, then multiply by the height.
  • Measure the radius and height in the same units—both in inches, both in centimeters, or both in feet—so your answer comes out in the right units.
  • A calculator with a π button makes the math faster and more accurate than rounding π to 3.14.

Step-by-Step Calculation

Start by measuring or finding the radius and height of your cylinder. Write both numbers down with their units (inches, centimeters, feet, whatever you're using).

Next, square the radius. This means multiply the radius by itself. If the radius is 5 inches, then r² = 5 × 5 = 25 square inches. Write this number down.

Then multiply that result by π. Using a calculator: 25 × 3.14159 = 78.54 (approximately). If you're using 3.14 instead, you get 25 × 3.14 = 78.5.

Finally, multiply that result by the height. If your cylinder is 10 inches tall, then 78.54 × 10 = 785.4 cubic inches. That's your volume.

Understanding Radius vs. Diameter

The radius is the distance from the center of the circle to the edge. The diameter is the distance all the way across the circle, passing through the center. The radius is always half the diameter.

If you measure across a can and get 6 inches, that's the diameter. The radius is 3 inches. Many people accidentally use the diameter in the formula and get a volume four times too large, so double-check which measurement you have.

If you're measuring a real object, use a ruler or measuring tape. Place it across the widest part of the circular opening or base. That's your diameter. Divide by 2 to get the radius.

Units and Your Final Answer

The units of your answer depend on the units you measured in. If you measure radius and height in inches, your volume comes out in cubic inches. If you measure in centimeters, you get cubic centimeters. If you measure in feet, you get cubic feet.

Cubic units (written as in³, cm³, or ft³) always appear in volume because volume is three-dimensional. A cubic inch is the space inside a cube that measures 1 inch on every side.

Make sure both your radius and height use the same units before you start. If the radius is in inches and the height is in feet, convert one of them first. For example, convert the height to inches, then do the math.

Common Mistakes to Avoid

The most frequent error is forgetting to square the radius. The formula is π × r² × h, not π × r × h. Squaring the radius means multiplying it by itself—don't skip that step.

Another common mistake is using the diameter instead of the radius. Remember: radius is half the diameter. If you use the full diameter in place of the radius, your answer will be four times too large.

A third mistake is mixing units. If your radius is in inches and your height is in feet, the formula won't work correctly. Convert everything to the same unit first.

Using a Calculator vs. Doing It by Hand

A basic calculator with a π button is the fastest and most accurate way. Enter the radius, press the multiply button, enter the radius again (to square it), press multiply, enter π, press multiply, enter the height, and press equals.

If you're doing it by hand without a calculator, use 3.14 for π to keep the arithmetic manageable. The answer won't be exact, but it will be close. For most real-world purposes—figuring out how much a tank holds, for example—3.14 is accurate enough.

Online calculators and spreadsheet programs (like Excel or Google Sheets) can also do this for you. In Google Sheets, you could type =PI()*5^2*10 to calculate the volume of a cylinder with radius 5 and height 10. The ^2 means "square".

Real-World Examples

A soup can has a radius of 2 inches and a height of 4 inches. Volume = π × 2² × 4 = π × 4 × 4 = 16π ≈ 50.27 cubic inches.

A water tank is 3 feet across (diameter), so the radius is 1.5 feet. The tank is 5 feet tall. Volume = π × 1.5² × 5 = π × 2.25 × 5 = 11.25π ≈ 35.34 cubic feet. To convert to gallons (a more useful unit for water), multiply by 7.48: about 264 gallons.

A cylindrical pipe has a radius of 1 centimeter and a length of 50 centimeters. Volume = π × 1² × 50 = 50π ≈ 157.08 cubic centimeters.

Frequently Asked Questions

What if my cylinder is lying on its side?

It doesn't matter. The formula is the same. The "height" is still the length of the cylinder from one end to the other, and the radius is still half the width of the circular end. Whether it's standing upright or lying down, the volume stays the same.

Do I need to use 3.14159 for pi, or is 3.14 good enough?

For most everyday purposes, 3.14 is fine. If you need more precision—for engineering or manufacturing—use more decimal places or let your calculator handle π. For a school assignment, check what your teacher asks for.

How do I find the radius if I only know the circumference?

The circumference is π × diameter, or 2πr. If you know the circumference, divide it by 2π to get the radius. For example, if the circumference is 31.4 inches, then radius = 31.4 ÷ (2 × 3.14) = 31.4 ÷ 6.28 ≈ 5 inches.

What's the difference between volume and surface area?

Volume is how much space is inside the cylinder (measured in cubic units). Surface area is how much material covers the outside (measured in square units). You need volume to know how much a tank holds; you need surface area to know how much paint to buy.

Can I use this formula for a cone or a sphere?

No. A cone's volume is (π × r² × h) ÷ 3—one-third of a cylinder with the same base and height. A sphere's volume is (4 × π × r³) ÷ 3. Each shape has its own formula.