Circumference of a Cylinder Calculator

Calculate cylinder base circumference, radius, and diameter with step-by-step solutions

Cylinder Base Measurements

Distance from center to edge

Distance across cylinder base

Perimeter around cylinder base

Cylinder Base Results

5.0000
Radius (r)
Distance from center
10.0000
Diameter (d)
Distance across
31.4159
Circumference (C)
Perimeter of base

Step-by-Step Solution

1.Given: Radius (r) = 5.0000 units
2.Calculate diameter: d = 2r = 2 × 5.0000 = 10.0000 units
3.Calculate circumference: C = 2πr = 2 × π × 5.0000 = 31.4159 units

Example Calculation

Problem

Find the circumference of a cylinder base with a radius of 5 cm.

Solution

Given: Radius (r) = 5 cm

Formula: C = 2πr

Calculate: C = 2 × π × 5 = 10π ≈ 31.416 cm

Result: The circumference of the cylinder base is approximately 31.416 cm.

Cylinder Base Formulas

Circumference

C = 2πr (from radius)
C = πd (from diameter)

Diameter

d = 2r (from radius)
d = C/π (from circumference)

Radius

r = d/2 (from diameter)
r = C/(2π) (from circumference)

Cylinder Properties

Base: A cylinder has two circular bases of equal size
Cross-section: All cross-sections parallel to the base are circles
Circumference: The perimeter of the circular base
Applications: Pipes, cans, tubes, and cylindrical containers

Understanding Cylinder Circumference

What is Cylinder Circumference?

The circumference of a cylinder refers to the perimeter of its circular base. Since a cylinder is formed by extending a circle along a height dimension, the circumference remains constant throughout the cylinder's height.

Key Relationships

  • Diameter = 2 × Radius: The diameter spans the full width of the base
  • C = 2πr: Circumference is proportional to radius
  • C = πd: Circumference equals π times diameter
  • Constant throughout height: All horizontal cross-sections have the same circumference

Practical Applications

  • Plumbing: Calculating pipe circumferences for fittings
  • Manufacturing: Designing cylindrical products and containers
  • Engineering: Structural design of columns and supports
  • Construction: Material calculations for cylindrical structures

Fun Fact: The circumference of a cylinder is the same as the width of the rectangle you'd get if you "unwrapped" the curved surface of the cylinder!

Cylinder Volume from Circumference

Step-by-Step Process

1. From circumference, find radius: r = C/(2π)

2. Calculate base area: A = πr²

3. Multiply by height: V = A × h = πr²h

Direct Formula

V = (C²h)/(4π)

Where C is circumference and h is height