Advanced Annulus Calculator

Advanced Annulus Calculator

Calculate area, circumference, and properties of annulus (ring-shaped) regions with interactive 3D visualizations

🔄 Annulus Input

Enter outer and inner radii or other known dimensions

📊 Annulus Properties

Complete geometric analysis

Enter annulus dimensions to see all calculated properties

📈 Geometric Analysis

Visual representation of annulus properties

📊 Radius Relationship

Comparison of inner and outer components

🎯 3D Annulus Visualization

Interactive 3D representation of the annulus

Drag to rotate • Scroll to zoom

Understanding Annulus

An annulus is a ring-shaped geometric figure formed by two concentric circles. It's the region between an outer circle and a smaller inner circle, commonly found in engineering, architecture, and natural phenomena.

Area Formula

Area = π(R² - r²) where R is the outer radius and r is the inner radius. This represents the difference between two circular areas.

Applications

Used in washer design, pipe cross-sections, planetary rings, architectural elements, and mechanical components requiring hollow circular geometry.

Centroid

For a uniform annulus, the centroid is at the geometric center. The center of mass depends on material distribution and thickness.

Moment of Inertia

I = π(R⁴ - r⁴)/4 about the central axis, important for rotational dynamics and structural analysis of ring-shaped objects.

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