# Annulus

Written by Jerry Ratzlaff on . Posted in Plane Geometry

The area between two concentric circles.

## Area of an Annulus formulas

 $$\large{ A = \pi \;r^2 - \pi \; R^2 }$$ $$\large{ A = \pi \; \left( r^2 - R^2 \right) }$$

### Where:

$$\large{ A }$$ = area

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius (inside diamester)

$$\large{ R }$$ = radius (outside diameter)

## Area of a sector of an Annulus formula

 $$\large{ A = \frac{ \pi \; \theta}{ 360^{\circ} } \; \left( R^2 - r^2 \right) }$$

### Where:

$$\large{ A }$$ = area

$$\large{ \theta }$$ = degree

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius (inside diamester)

$$\large{ R }$$ = radius (outside diameter)

## Breadth of an Annulus formula

 $$\large{ b = R - r }$$

### Where:

$$\large{ b }$$ = breadth

$$\large{ r }$$ = radius (inside diamester)

$$\large{ R }$$ = radius (outside diameter)

## Longest Interval of an Annulus formula

 $$\large{ l = 2 \; \sqrt{ R^2 - r^2 } }$$

### Where:

$$\large{ l }$$ = longest interval

$$\large{ r }$$ = radius (inside diamester)

$$\large{ R }$$ = radius (outside diameter)

## Perimeter of an Annulus formula

 $$\large{ P = 2 \; \pi \; \left( R + r \right) }$$

### Where:

$$\large{ P }$$ = perimeter

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius (inside diamester)

$$\large{ R }$$ = radius (outside diameter)