What Is an Annulus?

The two radii that matter

The geometry of an annulus comes from subtraction. Its area is found by subtracting the area of the inner disk from the area of the outer disk, which is why the two circles must share a center.

This page keeps both circles aligned around the same center so you can see that an annulus is defined by concentric structure, not merely by having one circle inside another.

For example, if the outer radius is 8 units and the inner radius is 5 units, the ring is not a circle with radius 3. Its area is π(8² minus 5²), because the entire inner disk is removed from the larger disk. The difference in radii describes thickness, not area.

An annulus with equal center but different radii can be used to model a washer. The outer disk supplies the full circular area, and the inner disk is the hole removed from it. Drawing both circles first makes the subtraction feel like a picture instead of a rule to recall.

• An annulus is the ring-shaped region between two concentric circles.
• Both circles in an annulus are concentric, meaning they share the same center.
• The annulus has an inner radius and an outer radius, and both matter in measurement problems.
• Annulus area is the difference between two circle areas, not the product or the average of the two radii.

Where annuli help

• Use annuli when working with washers, rings, circular tracks, and pipe cross-sections.
• Use them in area problems where one circular region is removed from a larger one.
• Use the concept whenever a circle-based figure has a hole in the middle but keeps the same center.

Annulus checks to make

• Do not call the region an annulus if the two circles are not concentric.
• Do not subtract radii and mistake that for the area of the ring.
• Do not confuse the thickness of the annulus with its full area.