Annulus Visualization
Results

Enter radius values and click Calculate to see results.

Step-by-Step Solution

Enter radius values and click Calculate to see step-by-step solution.

Formulas Used

Area of Annulus: A = π(r₂² - r₁²)

Outer Circumference: C₂ = 2πr₂

Inner Circumference: C₁ = 2πr₁

Total Circumference: C = C₁ + C₂ = 2π(r₁ + r₂)

Thickness: t = r₂ - r₁

Outer Diameter: D₂ = 2r₂

Inner Diameter: D₁ = 2r₁

Interactive Guide: Understanding the Annulus
What is an Annulus?

An annulus (or ring) is a flat, circular region bounded by two concentric circles. It's the shape that results when you take a circle and remove a smaller circle from its center.

Real-World Examples:
  • Washers and rings used in engineering
  • CD/DVD discs
  • Donut-shaped objects (topologically)
  • Planetary rings
Properties of an Annulus:

The key parameters of an annulus are its inner radius (r₁) and outer radius (r₂). These determine all other properties like area, circumference, and thickness.

Tips for Calculation:
  • Always ensure the outer radius is larger than the inner radius
  • The area formula derives from subtracting the area of the inner circle from the area of the outer circle
  • The total circumference includes both the inner and outer perimeters