Created By : Vaibhavi Kumari

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 01, 2023

This online calculator tool gives the radius, diameter, area, circumference of both inner and outer circles, and surface area of annulus. Provide a radius of the circles in the specified input fields and hit on the calculate button to navigate to the output page. ### Formulae of Annulus

The easy and useful formulas to calculate the circumference, area of the annulus are mentioned below. Check out all those formulas to solve the questions easily & fastly.

Below given are the most used annulus formulas in terms of radius

• The outer circumference of an annulus:
• CΓéü = 2πrΓéü
• The inner circumference of an annulus:
• CΓéé = 2πrΓéé
• The surface area of the Outer Circle:
• AΓéü = πrΓéü²
• The surface area of the Inner Circle:
• AΓéé = πrΓéé²
• The surface area of the annulus:
• A0 = AΓéü - AΓéé
• = πrΓéü² - πrΓéé²
• = π(rΓéü² - rΓéé²)

Annulus Calculations:

The following are the sets of formulas we used to find annulus parameters easily

• If inner, outer circle radii are given,
• Annulus outer circumference formula is CΓéü = 2πrΓéü
• Annulus inner circumference formula is CΓéé = 2πrΓéé
• Annulus outer circle area formula is AΓéü = πrΓéü²
• Annulus inner circle area formula is AΓéé = πrΓéé²
• Annulus area formula is A0 = π(rΓéü² - rΓéé²)
• Annulus outer circle diameter formula is dΓéü = 2rΓéü
• Annulus inner circle diameter formula is dΓéé = 2dΓéé
• If the radius of the outer circle, the circumference of the inner circle are given,
• Radius of inner circle formula is rΓéé = CΓéé / 2π
• Circumference of outer circle formula is CΓéü = 2πrΓéü
• The area of the outer circle formula is AΓéü = πrΓéü²
• The area of the inner circle formula is AΓéé = πrΓéé²
• Area of annulus formula is A0 = π(rΓéü² - rΓéé²)
• If the radius of the outer circle, area of the inner circle are given,
• The formula to calculate the radius of the inner circle is rΓéé = √(AΓéé / π )
• The formula to find the circumference of the outer annulus is CΓéü = 2πrΓéü
• The formula to get the circumference of the inner annulus is CΓéé = 2πrΓéé
• The formula to get the area of the outer circle is AΓéü = πrΓéü²
• The formula to compute area of annulus is A0 = π(rΓéü² - rΓéé²)
• If the circumference of the outer circle, the radius of the inner circle are given,
• Radius of outer annulus is rΓéü = CΓéü / 2π
• Circumference of the inner annulus is CΓéé = 2πrΓéé
• The area of the outer annulus is AΓéü = πrΓéü²
• Area of the inner annulus is AΓéé = πrΓéé²
• Area of annulus is A0 = π(rΓéü² - rΓéé²)
• If circumferences of both circles are known,
• The radius of the outer annulus formula is rΓéü = CΓéü / 2π
• Radius of inner annulus formula is rΓéé = CΓéé / 2π
• The area of the outer annulus formula is AΓéü = πrΓéü²
• The area of the inner annulus formula is AΓéé = πrΓéé²
• Surface area of annulus formula is A0 = π(rΓéü² - rΓéé²)
• If the circumference of the outer annulus, area of the inner annulus are given,
• Radius of outer annulus rΓéü = CΓéü / 2π
• Radius of inner annulus rΓéé = √(AΓéé / π )
• Circumference of inner annulus CΓéé = 2πrΓéé
• Area of outer annulus AΓéü = πrΓéü²
• Area of annulus A0 = π(rΓéü² - rΓéé²)
• If the area of the outer annulus, the radius of the inner annulus are known,
• Outer annulus radius is rΓéü = √(AΓéü / π )
• Outer annulus circumference is CΓéü = 2πrΓéü
• Inner annulus circumference is CΓéé = 2πrΓéé
• The inner annulus area is AΓéé = πrΓéé²
• Annulus area is A0 = π(rΓéü² - rΓéé²)
• If the area of the outer annulus, the circumference of the inner annulus are given,
• The radius of outer annulus rΓéü = √(AΓéü / π )
• Radius of inner annulus rΓéé = CΓéé / 2π
• Circumference of outer annulus CΓéü = 2πrΓéü
• Area of inner circle AΓéé = πrΓéé²
• Annulus area is A0 = π(rΓéü² - rΓéé²)
• If areas of both annulus are known,
• Outer annulus radius rΓéü = √(AΓéü / π )
• Inner annulus radius rΓéé = √(AΓéé / π )
• Outer annulus circumference CΓéü = 2πrΓéü
• Inner annulus circumference CΓéé = 2πrΓéé
• Area of annulus A0 = π(rΓéü² - rΓéé²)
• If the radius of the outer annulus, area of the annulus are known:
• Outer circle circumference is CΓéü = 2πrΓéü
• The outer circle area is AΓéü = πrΓéü²
• Inner circle area is AΓéé = AΓéü - A0
• Inner circle radius is rΓéé = √(AΓéé / π )
• Inner circle circumference is CΓéé = 2πrΓéé
• If the radius of the inner circle, the area of the annulus are given:
• Inner annulus circumference CΓéé = 2πrΓéé
• Inner annulus area AΓéé = πrΓéé²
• Outer annulus area AΓéü = A0 + AΓéé
• Outer annulus radius rΓéü = √(AΓéü / π )
• Outer annulus circumference CΓéü = 2πrΓéü
• If the area of the annulus, the circumference of the outer annulus are given,
• Outer annulus radius formula is rΓéü = CΓéü / 2π
• Outer annulus area formula is AΓéü = πrΓéü²
• Inner annulus area formula is AΓéé = AΓéü - A0
• Inner annulus radius formula is rΓéé = √(AΓéé / π )
• The inner annulus circumference formula is CΓéé = 2πrΓéé
• If the area of the annulus, the circumference of the inner annulus are given,
• Inner annulus radius formula is rΓéé = CΓéé / 2π
• The inner annulus area formula is AΓéé = πrΓéé²
• Outer annulus area formula is AΓéü = A0 + AΓéé
• Outer annulus radius formula is rΓéü = √(AΓéü / π )
• The outer annulus circumference formula is CΓéü = 2πrΓéü
• If the area of annulus, area of the outer annulus is given,
• Inner annulus area formula is AΓéé = AΓéü - A0
• Outer annulus radius formula is rΓéü = √(AΓéü / π )
• Inner annulus radius formula is rΓéé = √(AΓéé / π )
• The outer annulus circumference formula is CΓéü = 2πrΓéü
• The inner annulus circumference formula is CΓéé = 2πrΓéé
• If the area of the inner annulus, area of the annulus are given,
• Outer annulus area formula is AΓéü = A0 + AΓéé
• Outer annulus radius formula is rΓéü = √(AΓéü / π )
• Inner annulus radius formula is rΓéé = √(AΓéé / π )
• The outer annulus circumference formula is CΓéü = 2πrΓéü
• The inner annulus circumference formula is CΓéé = 2πrΓéé

### The Process to Find Annulus Area, Circumference

Below given are the easy steps to calculate the circumference and area of the annulus.

Circumference of Annulus:

• Get the radii of inner and outer circles.
• Double the radii and multiply it with the constant π.
• Obtained values will be the circumferences of both outer and inner circles.

Area of Annulus:

• Note down the radii of both circles from the question.
• Square the radius of inner and outer circles.
• Find the product of π and square of the radius.
• Obtained values will be the areas of both circles respectively.
• Subtract the area of the outer circle from the inner circle area to find the annulus area.

### Example Questions on Annulus

Example 1: Calculate the area, circumference of the annulus? The outer circle radius is 12 cm and the inner circle radius is 7 cm.

Solution:

Given that,

The outer circle radius is rΓéü = 12 cm

The inner circle radius rΓéé = 7 cm

Circumference of outer circle CΓéü = 2πrΓéü

= 2 * 3.14 * 12

= 75.36

Circumference of inner circle CΓéé = 2πrΓéé

= 2 * 3.14 * 7

= 43.96

Area of the outer circle AΓéü = πrΓéü²

= 3.14 * 12²

= 3.14 * 12 * 12

= 452.16

Area of the inner circle AΓéé = πrΓéé²

= 3.14 * 7²

= 3.14 * 7 * 7

= 153.86

Surface area of the annulus A0 = AΓéü - AΓéé

= 452.16 - 153.86

= 298.3

∴ The area of the annulus is 298.3 cm²

Example 2: Find area, the circumference of both circles? If the area of the inner circle is 120 m² and the radius of the outer circle is 8 m.

Solution:

Given that,

The radius of the outer circle rΓéü = 8 m

Area of inner circle AΓéé = 120 m²

Circumference of outer circle CΓéü = 2πrΓéü

= 2 * 3.14 * 8

= 50.24

Area of the outer circle AΓéü = πrΓéü²

= 3.14 * 8²

= 3.14 * 8 * 8

= 200.96

Radius of the inner circle rΓéé = √(AΓéé / π)

= √(120 / 3.14 )

= √38.21

= 6.18

Circumference of inner circle CΓéé = 2πrΓéé

= 2 * 3.14 * 6.18

= 38.81

Surface area of the annulus A0 = AΓéü - AΓéé

= 200.96 - 120

= 80.96

∴ The area of the annulus is 80.96 m², the radius of the inner circle is 6.18 m.

Check many more geometry concepts from Areavolumecalculator.com and clear all your queries.

### FAQs on Annulus Calculator

1. How do you define the annulus?

An annulus is a ring-shaped object bounded by two concentric circles of different radii. The examples of an annulus are a disk having a circular hole in the middle. There is a common center point for both concentric circles. The dimensions of an annulus are defined by radii R and r.

2. What is the formula to find the area of an annulus using a diameter?

The area of the annulus is A = π/4(D² - d²). Where D is the outer circle diameter, d is the inner circle diameter.

3. How do you solve annulus for the outer and inner radius?

We know that the annulus area is A = π(R² - r²)

Outer circle radius R = √(r² + (A/π))

Inner circle radius r = √(R² - (A/π))