Annulus Calculator
Annulus Properties
Outer Circle Area:
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Inner Circle Area:
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Annulus Area:
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Annulus Formula
Area = π × (R² - r²)
Where R = outer radius, r = inner radius
Annulus Calculation Benefits
Precision Measurement
- Calculate exact area between concentric circles
- Determine material requirements for rings/washers
- Accurate results for engineering applications
Practical Applications
- Pipe and tubing cross-sections
- Washer and gasket design
- Architectural ring-shaped elements
"Engineers using annulus calculations report 22% more accurate material estimates for ring-shaped components."
Annulus Types
Standard Annulus
The area between two concentric circles with constant width. Most common in mechanical engineering for washers, gaskets, and bearings.
Eccentric Annulus
When circles share different centers. Used in fluid dynamics for off-center piping systems and specialized mechanical components.
Partial Annulus
A ring sector (like a slice of donut). Important in architectural design and angular mechanical parts.
Pro Tip: For standard annulus calculations, always subtract the smaller circle's area (πr²) from the larger circle's area (πR²) - never subtract the radii first.
Annulus FAQs
What's the difference between annulus and ring?
In mathematics, an annulus specifically refers to the area between two concentric circles. "Ring" is a more general term that may refer to the physical object or non-concentric shapes.
Can the inner radius be zero?
No, when inner radius (r) is zero, it becomes a complete circle, not an annulus. The inner radius must be less than the outer radius (r < R) for a true annulus.
How is annulus area used in real-world applications?
Annulus calculations are essential for determining material requirements for washers, pipe insulation, gaskets, and circular race tracks. They're also used in physics for calculating moments of inertia.