Cylinder Volume Calculator

Calculate the volume of a cylinder using V = pi r2 h. Enter radius and height, select your unit, and see surface area as a bonus.

Enter Cylinder Dimensions

Result

Volume
942.477796
cubic units
Diameter10
Base Area78.539816
Circumference31.415927
Lateral Surface Area376.991118
Total Surface Area534.07075
Volume in LitersN/A

Step-by-Step Solution

V = pi r^2 h = pi x 5^2 x 12 = 942.477796

Understanding Cylinder Volume

The volume of a cylinder measures the amount of three-dimensional space inside the cylindrical shape. A cylinder is formed by two parallel circular bases connected by a curved surface at a fixed distance (the height). The volume formula V = pi r2 h reflects this structure: pi r2 gives the area of the circular base, and multiplying by h stacks those circular layers up to the full height.

Cylinders are among the most common shapes in engineering, manufacturing, and everyday life. From beverage cans and water pipes to hydraulic cylinders and grain silos, understanding how to calculate cylinder volume is an essential practical skill.

Cylinder Formulas

Volume

The space enclosed within the cylinder.

V = pi r2 h

Base Area

The area of one circular end.

A = pi r2

Lateral Surface Area

The curved side surface of the cylinder.

LSA = 2 pi r h

Total Surface Area

Lateral surface plus both circular bases.

SA = 2 pi r h + 2 pi r2

Circumference

The perimeter of the circular base.

C = 2 pi r

Volume from Diameter

Using diameter instead of radius.

V = pi (d/2)2 h = pi d2 h / 4

Step-by-Step: How to Calculate Cylinder Volume

  1. Measure the radius (r): The radius is the distance from the center of the circular base to its edge. If you know the diameter, divide it by 2 to get the radius.
  2. Measure the height (h): The height is the perpendicular distance between the two circular bases.
  3. Square the radius: Calculate r2 = r x r.
  4. Multiply by pi: Calculate pi x r2 to get the base area.
  5. Multiply by the height: Multiply the base area by h to get the volume.

Volume and Capacity Conversions

Converting between volume units is common when working with cylinders:

  • 1 cm3 = 1 mL (milliliter)
  • 1,000 cm3 = 1 liter
  • 1 m3 = 1,000 liters
  • 1 in3 = 16.387 cm3
  • 1 ft3 = 28.317 liters
  • 1 US gallon = 3,785.41 cm3 = 3.785 liters

Practical Applications

  • Water Tanks: Calculating how much water a cylindrical tank can hold.
  • Pipes: Determining the flow capacity of cylindrical pipes.
  • Cooking: Finding the volume of cylindrical baking pans and pots.
  • Construction: Computing concrete needed for cylindrical pillars and columns.
  • Chemistry: Measuring liquid volumes in graduated cylinders.
  • Fuel Storage: Calculating the capacity of cylindrical fuel tanks.

Cylinder vs. Other Shapes

A cylinder with a given base area and height has the same volume formula concept as a prism: V = base area x height. What makes the cylinder special is that its base is a circle, so the base area is pi r2. For comparison, a cone with the same base and height has exactly one-third the volume of the cylinder (V = pi r2 h / 3), while a sphere with the same radius has volume V = 4/3 pi r3.

Oblique Cylinders

An oblique cylinder is tilted so the axis is not perpendicular to the base. Remarkably, the volume formula remains the same: V = pi r2 h, where h is the perpendicular height (not the slant height). This is a consequence of Cavalieri's principle, which states that if two solids have the same cross-sectional area at every height, they have the same volume.

Tips for Accurate Cylinder Volume Calculations

  • Always use the radius (half the diameter), not the diameter, in the formula.
  • Make sure radius and height are in the same units before calculating.
  • Volume is in cubic units -- if your inputs are in cm, the volume is in cm3.
  • For hollow cylinders (pipes), calculate V_outer - V_inner.
  • Use the perpendicular height for oblique cylinders, not the slant height.