# Annulus Calculator

> Calculate the area and boundary lengths of a ring between two concentric circles.

Page: https://askcalculators.com/calculator/annulus-calculator/
Definition: https://askcalculators.com/calculator/annulus-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/annulus-calculator/schema.json
Version: 1.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/annulus-calculator/?outerRadius=10&innerRadius=6

## Inputs
- outerRadius: Outer radius R; type=number; required; default=10; min=0.000001
- innerRadius: Inner radius r; type=number; required; default=6; min=0

## Outputs
- area: Annulus area; format=number; primary
- outerCircumference: Outer circumference; format=number
- innerCircumference: Inner circumference; format=number
- width: Ring width; format=number

## Formula
area = π(R² − r²)

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.