Area of an annulus - Math Open Reference

Area of an annulus

The number of square units it takes to completely fill an annulus.

Try this Drag the orange dots to move and resize the circles. As the size of the circles change, the area is recalculated.

(If there is no image below, see support page.)

Area formula

The area of the annulus is the area of the ring-shaped space between the two circles that define it. In the figure above it is the number of gray square units it takes to fill the annulus. This area is the area of the entire disk, minus the area of the 'hole' in the middle. ( See Area of a Circle):

where:
R is the radius of the outer circle
H is the radius of the inner 'hole'
π is Pi, approximately 3.142

which simplifies a little to:

Try this

In the figure above, click on "hide details"
Drag the orange dots on the edge of the circles to make a random-size annulus.
Now try to estimate the area of the annulus just by looking at the squares inside it
Calculate the area using the formula

When you done click "show details" to see how close you got.

Other circle topics

General

Angles in a circle

Arcs