Annulus(Ring) Calculator

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

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 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.

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))