What Is the Annulus (Ring) Area Calculator?
An annulus is the 2D geometric region bounded by two concentric circles of differing radii sharing a common center point.
Everyday examples include flat metal washers, vehicle brake rotors, planetary rings, and pipe wall cross-sections.
How Does the Annulus (Ring) Area Calculator Work?
The calculator computes area by subtracting inner circle area from outer circle area: A = π·(R² - r²).
Ring width (thickness) is w = R - r, while mean radius is R_avg = (R + r) / 2.
Annulus (Ring) Area Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Annulus area is calculated by subtracting the inner circular hole area (πr²) from the outer circle area (πR²).
How to Use the Annulus (Ring) Area Calculator
- Enter the outer radius R.
- Enter the inner hole radius r (must be less than R).
- Examine the net ring area, radial wall width, and both inner and outer circumferences.
Step-by-Step Example Calculation
Washer (R = 10, r = 6)
Input Values:
Understanding Your Result
The ring area can also be visualized as a rectangle of length equal to average circumference 2π·R_avg and height equal to width w.
Factors That Affect the Result
- Wall Thickness: As inner radius approaches outer radius, area scales proportionally to width w.
When Should You Use This Calculator?
- Sizing flat mechanical washers, flange gaskets, and hydraulic seals.
- Computing pipe wall cross-sectional steel areas for structural and fluid flow analysis.
Assumptions & Limitations
- Assumes concentric circles sharing identical center coordinates.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact analytical circular area subtraction.