annulus r and R  

An annulus is a flat shape like a ring.

Its edges are two circles that have the same center.


Washers (various)
The face of a metal washer is an annulus

Something shaped like an annulus is said to be annular.

Saturn has annular rings:



Because it is a circle with a circular hole, you can calculate the area by subtracting the area of the "hole" from the big circle's area:

annulus area pi R^2 - pi r^2

Area = πR2πr2
= π( R2 − r2 )


annulus pipe

Example: a steel pipe has an outside diameter (OD) of 100mm and an inside diameter (ID) of 80mm, what is the area of the cross section?

Convert diameter to radius for both outside and inside circles:

Now calculate area:

Area = π( R2 - r2 )
Area = 3.14159... × ( 502 − 402 )
Area = 3.14159... × (2500 − 1600)
Area = 3.14159... × 900
Area = 2827 mm2 (to nearest mm2)