Cylinder Calculator

Calculate volume, surface area, height, radius, and diameter of any cylinder instantly

Calculation Results

Enter a cylinder measurement to calculate all properties.

Cylinder Diagram

r = 0 h = 0 V = 0 S = 0

The Cylinder: A Powerful 3D Geometric Shape

A cylinder is a three-dimensional geometric figure with two parallel circular bases connected by a curved surface. It's one of the most commonly encountered solids in both nature and industry.

Key Properties of a Cylinder

  • Radius (r) – The radius of the circular base.
  • Height (h) – The distance between the two circular bases.
  • Base Area (Ab) – The area of one circular base (Ab = πr²).
  • Lateral Surface Area (LSA) – The area of the side surface (LSA = 2πrh).
  • Total Surface Area (TSA) – Sum of lateral area and two bases (TSA = 2πr(h + r)).
  • Volume (V) – The space enclosed inside the cylinder (V = πr²h).

Mathematical Equations of a Cylinder

  • Volume: V = πr²h
  • Lateral Surface Area: LSA = 2πrh
  • Total Surface Area: TSA = 2πr(h + r)

Why Are Cylinders Important?

  • Engineering & Construction - Used in tanks, pipes, pillars, and rollers.
  • Physics - Appear in calculations involving pressure, fluid volume, and torque.
  • Manufacturing - Common in bottles, cans, batteries, and engine parts.
  • Nature & Astronomy - Found in tree trunks, bamboo, and planetary magnetospheres.

Facts About Cylinders

  • Cylinders are one of the three basic 3D shapes, along with cones and spheres.
  • The ancient Greeks studied cylinders in detail in Euclid’s *Elements*.
  • Cylindrical symmetry simplifies many physics and engineering problems.

Cylinders are practical, symmetrical, and versatile shapes. Understanding their geometry is essential in design, science, and industry.

r

Radius (r)

h

Height (h)

Ab

Base Area (πr²)

LSA

Lateral Surface Area

TSA

Total Surface Area

V

Volume (V)

Cylinder Formulas

  • Base Area (Ab): πr²
  • Lateral Surface Area (LSA): 2πrh
  • Total Surface Area (TSA): 2πr(h + r)
  • Volume (V): πr²h

Where π (pi) ≈ 3.141592653589793

How to Use the Cylinder Calculator

The Cylinder Calculator helps compute surface areas and volume based on input values. Here's how to use it:

1 Select What You Know

Choose the known values combination:

  • Radius (r)
  • Height (h)
  • Volume
  • Surface Area
  • Lateral Area

2 Enter the Values

Type in positive numeric values for radius and/or height.

Example: r = 3, h = 10

3 Click "Calculate"

The calculator will compute:

  • Base Area
  • Lateral Surface Area
  • Total Surface Area
  • Volume

Example Use Cases

  • Calculate the volume of a water tank (cylindrical).
  • Determine the material needed to wrap a can.
  • Find internal volume for hydraulic cylinders.

Example Calculations

  • Example 1: r = 4 units, h = 10 units

    • Volume = π × 4² × 10 ≈ 502.65 units³
    • LSA = 2π × 4 × 10 ≈ 251.33 units²
    • TSA = 2π × 4 (10 + 4) ≈ 351.86 units²

  • Example 2: r = 7 cm, h = 15 cm

    • Volume ≈ 2309.44 cm³
    • LSA ≈ 659.73 cm²
    • TSA ≈ 1040.57 cm²

Frequently Asked Questions

1. What's the difference between LSA and TSA?

LSA (Lateral Surface Area): Area of the curved surface only (side).

TSA (Total Surface Area): LSA + Area of both circular bases.

2. How do I find volume if I know TSA?

You need the radius or height as well. TSA alone isn't enough unless paired with another value.

3. Are cylinders always vertical?

No, a cylinder can be oriented any way. A horizontal cylinder is common in tanks and drums.

4. What are real-world uses of cylinders?
  • Water pipes and gas tanks
  • Engine cylinders and pistons
  • Food cans and storage drums
  • Architectural columns

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