Annulus
An annulus is an inner region between two concentric circles i.e. two or more circles sharing the same center point. The annulus is shaped like a ring and has many applications in mathematics that we will be learning in this article. Some of the reallife examples are a doughnut, finger rings. etc. Let us learn more about the shape of the annulus and solve a few examples to understand the concept better.
1.  Definition of Annulus 
2.  Area of Annulus 
3.  Perimeter of Annulus 
4.  FAQs on Annulus 
Annulus Definition
An annulus is a twodimensional flat figure shaped in a circular form which is constructed by two concentric circles. The region or the area formed in between these two concentric circles is called the annulus. Since it is a flat figure in a circular form, the edges are two circles with the same center. It is considered a circular disk having a circular hole in the middle.
Annulus Meaning
The word annulus is derived from a Latin word, 'annuli', meaning little rings. The shape of the annulus is flat and circular with a hole in between, much like a throw ring or a circular disc. Look at the image below showing two circles i.e. one small circle also called an inner circle and a big circle also called the outer circle. The point which is marked as red is the center of both circles. The shaded colored area, between the boundary of these two circles, is known as an annulus.
Area of the Annulus
The annulus area is the area of the ringshaped space i.e. the enclosed region between the two concentric circles. To calculate the area of the annulus, we need the area of both the inner circle and the outer circle. The dimensions of an annulus are defined by the two radii R, and r, which are the radii of the outer ring and the inner ring respectively. Once the measurements of both the radii are known, we can calculate the area by subtracting the area of the small circle from the big circle. Hence, the formula used for finding the area of the annulus is:
Area of Outer Circle = πR^{2}
Area of Inner Circle = πr^{2}
Area of Annulus = Area of Outer Circle – Area of Inner Circle
Therefore, Area of Annulus = π(R^{2}r^{2}) square units, or it can be written as π(R+r)(Rr) square units, where R is the radius of the outer circle, r is the radius of the inner circle, and π(pi) is approximately 3.142. Look at the image below, the area of the outer (bigger) circle  the area of the inner (smaller) circle = the area of the annulus.
Annulus Perimeter
The perimeter is the distance around the 2D shape. Since the annulus is a flat circular shape constructed by two concentric circles, it can also be considered as a ring. Therefore, an open ring can be considered as the topological equivalent of a cylinder and a punctured plane. Similar to the area, to find the perimeter of the annulus we need to consider both the inner circle and the outer circle. So, the perimeter of the ring or annulus is equal to the sum of the radii of the large and small circles multiplied by 2π. The formula for finding the perimeter is:
Perimeter of Annulus (P) = 2π(R+r) units, where R is the radius of the outer circle, r is the radius of the inner circle, and π (pi) is approximately 3.142.
Related Topics
Listed below are a few relatable topics to the annulus, take a look!
Annulus Examples

Example 1: Calculate the area of the annulus if the outer radius is 15 units and the inner radius is 8 units.
Solution: Given that outer radius (R) = 15 units and inner radius (r) = 8 units.
Area of outer circle = πR^{2} = 3.142 × 15 × 15 = 706.95 units
Area of inner circle = πr^{2} = 3.142 × 8 × 8 = 201.088 units
The formula to find the area of an annulus is (area of the outer circle – area of the inner circle) square units.
Area = (706.95 – 201.088) square units
Therefore, the required area is 505.862 square units.

Example 2: If the outer radius of a ring is 10 units and the inner radius of a ring is 3 units, what would be the perimeter of the ring?
Solution: We already know that the perimeter of the annulus = 2π(R+r) and it is given that R = 10 units and r = 3 units.
P = 2 × 3.142 (10 + 3)
P = 6.284 × 13
P = 81.692 units
Therefore, the perimeter of the ring is 81.692 units.

Example 3: A steel pipe has an outer diameter of 80 units and an inner diameter of 60 units, what is the area of the crosssection?
Solution: As we know the diameter is twice the radius. So we divide the value by 2 to obtain the radius.
Outer radius, R = 80/2 = 40 units
Inner radius, r = 60/2 = 30 units
Area of Annulus = π(R^{2}r^{2}) square units
A = 3.142 (40^{2}  30^{2})
A = 3.142 (1600  900)
A = 3.142 × 700
A = 2199.4 units^{2}
Therefore, the area of the crosssection of the pipe is 2199.4 units^{2}.
FAQs on Annulus
What is the Meaning of the Word Annulus?
The word annulus is derived from the Latin word annuli which means little rings. It is a 2D flat figure which is circular in nature but a hole in between like a doughnut. An annulus is the region enclosed between the boundary of these two circles.
What is Annulus Area?
The annulus area is the area of the ringshaped i.e. the region enclosed between the two concentric circles. To calculate the area of the annulus, the areas of both the inner circle and the outer circle are required.
Area of Outer Circle = πR^{2}
Area of Inner Circle = πr^{2}
Based on these, the formula for the area of the annulus is area of outer circle – area of inner circle. Therefore, Area of Annulus = π(R^{2}r^{2}) square units, where R is the radius of the outer circle, r is the radius of the inner circle, and π (pi) is approximately 3.142.
What is the Perimeter of the Annulus?
Annulus perimeter is considered as the entire distance around the 2D shape including both the inner circle and the outer circle. The formula to find the perimeter of the annulus is 2π(R+r) units, where R is the radius of the outer circle, r is the radius of the inner circle, and π (pi) is approximately 3.142.
Is a Circle an Annulus?
In mathematics, an annulus is a region between two concentric circles. It is shaped like a ring or a donut. A circle is not an annulus since it is a completely closed figure in a circular manner, whereas an annulus is a circularshaped figure but with a hole in between.
What is Annulus Radius?
The annulus radius is the difference between the radius of the outer circle and the inner circle. Since an annulus is constructed by two concentric circles, the radius of both the circles is required. The dimensions of the annulus radius are derived from the radii of the outer circle and inner circle with R and r as the measures respectively.
What Dimension is an Annulus?
An annulus is a twodimensional shape that is flat and circular in nature. It is constructed by two concentric circles with a hole in between and that enclosed region is called the annulus.
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