Cylinder Volume Calculator

Enter a cylinder's radius and height to get its volume (V = πr²h), total surface area, and lateral surface area, plus an optional material cost estimate.

Quick Facts

Volume formula
V = πr²h
Base area (πr²) times height; doubling the radius quadruples the volume.
Total surface area
A = 2πr(r + h)
Two circular ends (2πr²) plus the curved side (2πrh).
Lateral surface area
A = 2πrh
The curved side only, unrolled into a rectangle of width 2πr and height h.

Your Results

Calculated
Volume
-
V = πr²h, in cubic units
Total Surface Area
-
A = 2πr(r + h)
Lateral Surface Area
-
A = 2πrh (side only)
Estimated Material Cost
-
Volume × cost per cubic unit

Ready

Enter a radius, height, and unit, then press Calculate.

Formula and Method for Cylinder Volume

Volume of a Cylinder:

V = π × r² × h

r = radius of the circular base; h = height (the perpendicular distance between the two circular ends)

A cylinder is a solid with two parallel, congruent circular bases connected by a curved lateral surface. Because every cross-section parallel to the base is an identical circle, its volume is simply the area of that circular base (πr²) multiplied by the height: V = πr²h. This calculator also derives the total surface area and lateral (side-only) surface area from the same radius and height, plus an optional material cost estimate from the volume.

How the calculation works

Enter the radius and height and choose the unit they are measured in. The calculator squares the radius and multiplies by π and the height to get the volume (in cubic units, such as in³ or m³). It multiplies the radius by height and by 2π to get the lateral surface area (A = 2πrh) — the curved side, which unrolls into a rectangle of width 2πr (the base's circumference) and height h. Adding the two circular ends (each πr², so 2πr² together) gives the total surface area: A = 2πr² + 2πrh, which factors to A = 2πr(r + h). If you enter a cost per cubic unit, the tool multiplies it by the volume to estimate total material cost.

Common mistakes

  • Radius vs. diameter: the formula uses radius, not diameter. If you only know the diameter, divide it by 2 first — using diameter directly overstates the volume by a factor of 4.
  • Confusing volume with surface area: a cylinder with a 3 in radius and 10 in height has a volume of about 282.7 in³, but a total surface area of only about 245.0 in² — different units (cubic vs. square) and different quantities entirely.
  • Mixing units: keep the radius and height in the same unit — convert inches to feet, or centimeters to meters, before entering the values.
  • Lateral vs. total surface area: lateral area (2πrh) excludes the two circular ends; total area (2πr(r + h)) includes them. Use lateral area when only the side is coated or wrapped.

Real-world applications

  • Tank, pipe, and can sizing use volume directly to determine liquid, gas, or material capacity.
  • Packaging and labeling use lateral surface area to size a label that wraps around a cylindrical container without covering the top or bottom.
  • Painting, coating, or plating a cylindrical tank or column uses total surface area to estimate how much material is needed.
  • Concrete and construction use cylinder volume to estimate material for columns, pilings, and cylindrical footings.

Frequently Asked Questions

What is the formula for the volume of a cylinder?
The volume of a cylinder equals the area of its circular base times its height: V = πr²h, where r is the radius and h is the height. For example, a cylinder with a 3 in radius and 10 in height has a volume of π × 3² × 10 ≈ 282.74 in³.
How do I find the surface area of a cylinder?
Total surface area adds the areas of the two circular ends to the lateral (side) surface: A = 2πr² + 2πrh, which factors to A = 2πr(r + h).
What is the difference between total and lateral surface area?
Lateral surface area (2πrh) is just the curved side of the cylinder, unrolled into a rectangle. Total surface area (2πr(r + h)) adds the two flat circular ends (2πr² combined). Use lateral area for wrapping or labeling the side only, and total area for full coverage such as painting or coating.
How do I convert cylinder volume between units?
Multiply the volume by the linear conversion factor cubed, since volume scales with the cube of length. For example, 1 m³ = (3.2808 ft)³ ≈ 35.315 ft³, so multiply a volume in m³ by about 35.315 to get ft³.

Related calculators