Cylinder Calculator

Enter a positive numerical value for the radius of the cylinder.

Enter a positive numerical value for the height of the cylinder.

Volume

Curved Surface Area

Total Surface Area

Formulas:
Volume (V) = $V = \pi r^2 h$
Curved Surface Area (CSA) = $CSA = 2 \pi r h$
Total Surface Area (TSA) = $TSA = 2 \pi r (h+r)$

Understanding Cylinder Calculations: Volume, Surface Area, and More

Welcome to our comprehensive Cylinder Calculator, your go-to online tool for efficiently determining the various properties of a cylinder. This powerful calculator simplifies complex geometric calculations, providing instant results for cylinder volume, curved surface area of a cylinder (also known as lateral surface area), and the total surface area of a cylinder. Whether you're a student, engineer, or simply curious, our tool offers precise calculations and detailed explanations.

What is a Cylinder?

A cylinder is a fundamental three-dimensional geometric shape, characterized by two parallel circular bases of the same size connected by a curved surface. Think of common objects like a soda can, a battery, or a pipe – these are all examples of cylinders. Understanding its dimensions, namely its radius (r) and height (h), is crucial for any cylinder calculation.

How to Calculate Cylinder Volume

The volume of a cylinder represents the amount of three-dimensional space it occupies or the capacity it holds. It's a measure of how much liquid or material can fit inside. The formula for the volume of a cylinder is derived from multiplying the area of its circular base by its height.

The formula for cylinder volume is:

$V = \pi r^2 h$

  • $V$: Volume of the cylinder
  • $\pi$ (Pi): Approximately 3.14159
  • $r$: Radius of the cylinder's base
  • $h$: Height of the cylinder

For example, if you have a cylinder with a radius of 4 cm and a height of 10 cm, the volume calculation would be: $V = \pi \times (4 \text{ cm})^2 \times 10 \text{ cm} = 160\pi \text{ cm}^3$. Our calculator handles these steps for you, presenting the final cylinder volume with ease.

Calculating the Surface Area of a Cylinder

The surface area of a cylinder refers to the total area of its outer surface. This includes both the curved side and the two circular bases. It's often broken down into two components: the curved surface area and the total surface area.

Curved Surface Area of a Cylinder (Lateral Surface Area)

The curved surface area of a cylinder (or lateral surface area) is the area of the curved side only, excluding the top and bottom circular bases. Imagine unrolling the side of a can into a rectangle – its area would be the curved surface area.

The formula for curved surface area of cylinder is:

$CSA = 2 \pi r h$

  • $CSA$: Curved Surface Area
  • $\pi$ (Pi): Approximately 3.14159
  • $r$: Radius of the cylinder's base
  • $h$: Height of the cylinder

Total Surface Area of a Cylinder

The total surface area of a cylinder is the sum of its curved surface area and the areas of its two circular bases. This calculation is essential when you need to know the total material required to construct a cylindrical object.

The formula for total surface area of cylinder is:

$TSA = 2 \pi r (h+r)$

  • $TSA$: Total Surface Area
  • $\pi$ (Pi): Approximately 3.14159
  • $r$: Radius of the cylinder's base
  • $h$: Height of the cylinder

Our tool simplifies these cylinder area calculations, providing accurate results instantly.