Annulus

Annulus with outer radius R and inner radius r sharing a common center point  

An annulus is a flat shape like a ring.

Its edges are two circles that have the same center.

Three flat metal washers of different sizes demonstrating an annular shape
The face of a metal washer is an annulus

Something shaped like an annulus is said to be annular.

Saturn has annular rings:

Planet Saturn showing its wide, flat concentric rings

Area

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:

Diagram showing a large circle minus a smaller circle to equal the shaded annulus area

Area = πR2 − πr2
= π( R2 − r2 )

Steel pipe cross-section showing its solid outer wall and hollow circular interior

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

Convert diameter to radius for both outside and inside circles:

  • R = 100 mm / 2 = 50 mm
  • r = 80 mm / 2 = 40 mm

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)

The equivalent formula for diameters is:

Area = π4( D2 − d2 )

Maybe you could try the previous example using that formula?

3234, 9054, 9055, 9056, 9057, 9058, 9059, 9060, 9061, 224
Circle Area of Circle Geometry Index