Annulus(Ring) Calculator

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.


Annulus Calculator is an easy to operate user-friendly handy tool that gives the circumference, area of outer, inner circles and annulus in a fraction of seconds. This page helps you to learn about the annulus concept easily. You can find the simple formulae and step by step procedure to calculate the diameter, circumference, and area of both circles, the surface area of the annulus.

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:
    • C₁ = 2πr₁
  • The inner circumference of an annulus:
    • C₂ = 2πr₂
  • The surface area of the Outer Circle:
    • A₁ = πr₁²
  • The surface area of the Inner Circle:
    • A₂ = πr₂²
  • The surface area of the annulus:
    • A0 = A₁ - A₂
    • = πr₁² - πr₂²
    • = π(r₁² - r₂²)

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 C₁ = 2πr₁
    • Annulus inner circumference formula is C₂ = 2πr₂
    • Annulus outer circle area formula is A₁ = πr₁²
    • Annulus inner circle area formula is A₂ = πr₂²
    • Annulus area formula is A0 = π(r₁² - r₂²)
    • Annulus outer circle diameter formula is d₁ = 2r₁
    • Annulus inner circle diameter formula is d₂ = 2d₂
  • If the radius of the outer circle, the circumference of the inner circle are given,
    • Radius of inner circle formula is r₂ = C₂ / 2π
    • Circumference of outer circle formula is C₁ = 2πr₁
    • The area of the outer circle formula is A₁ = πr₁²
    • The area of the inner circle formula is A₂ = πr₂²
    • Area of annulus formula is A0 = π(r₁² - r₂²)
  • 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 r₂ = √(A₂ / π )
    • The formula to find the circumference of the outer annulus is C₁ = 2πr₁
    • The formula to get the circumference of the inner annulus is C₂ = 2πr₂
    • The formula to get the area of the outer circle is A₁ = πr₁²
    • The formula to compute area of annulus is A0 = π(r₁² - r₂²)
  • If the circumference of the outer circle, the radius of the inner circle are given,
    • Radius of outer annulus is r₁ = C₁ / 2π
    • Circumference of the inner annulus is C₂ = 2πr₂
    • The area of the outer annulus is A₁ = πr₁²
    • Area of the inner annulus is A₂ = πr₂²
    • Area of annulus is A0 = π(r₁² - r₂²)
  • If circumferences of both circles are known,
    • The radius of the outer annulus formula is r₁ = C₁ / 2π
    • Radius of inner annulus formula is r₂ = C₂ / 2π
    • The area of the outer annulus formula is A₁ = πr₁²
    • The area of the inner annulus formula is A₂ = πr₂²
    • Surface area of annulus formula is A0 = π(r₁² - r₂²)
  • If the circumference of the outer annulus, area of the inner annulus are given,
    • Radius of outer annulus r₁ = C₁ / 2π
    • Radius of inner annulus r₂ = √(A₂ / π )
    • Circumference of inner annulus C₂ = 2πr₂
    • Area of outer annulus A₁ = πr₁²
    • Area of annulus A0 = π(r₁² - r₂²)
  • If the area of the outer annulus, the radius of the inner annulus are known,
    • Outer annulus radius is r₁ = √(A₁ / π )
    • Outer annulus circumference is C₁ = 2πr₁
    • Inner annulus circumference is C₂ = 2πr₂
    • The inner annulus area is A₂ = πr₂²
    • Annulus area is A0 = π(r₁² - r₂²)
  • If the area of the outer annulus, the circumference of the inner annulus are given,
    • The radius of outer annulus r₁ = √(A₁ / π )
    • Radius of inner annulus r₂ = C₂ / 2π
    • Circumference of outer annulus C₁ = 2πr₁
    • Area of inner circle A₂ = πr₂²
    • Annulus area is A0 = π(r₁² - r₂²)
  • If areas of both annulus are known,
    • Outer annulus radius r₁ = √(A₁ / π )
    • Inner annulus radius r₂ = √(A₂ / π )
    • Outer annulus circumference C₁ = 2πr₁
    • Inner annulus circumference C₂ = 2πr₂
    • Area of annulus A0 = π(r₁² - r₂²)
  • If the radius of the outer annulus, area of the annulus are known:
    • Outer circle circumference is C₁ = 2πr₁
    • The outer circle area is A₁ = πr₁²
    • Inner circle area is A₂ = A₁ - A0
    • Inner circle radius is r₂ = √(A₂ / π )
    • Inner circle circumference is C₂ = 2πr₂
  • If the radius of the inner circle, the area of the annulus are given:
    • Inner annulus circumference C₂ = 2πr₂
    • Inner annulus area A₂ = πr₂²
    • Outer annulus area A₁ = A0 + A₂
    • Outer annulus radius r₁ = √(A₁ / π )
    • Outer annulus circumference C₁ = 2πr₁
  • If the area of the annulus, the circumference of the outer annulus are given,
    • Outer annulus radius formula is r₁ = C₁ / 2π
    • Outer annulus area formula is A₁ = πr₁²
    • Inner annulus area formula is A₂ = A₁ - A0
    • Inner annulus radius formula is r₂ = √(A₂ / π )
    • The inner annulus circumference formula is C₂ = 2πr₂
  • If the area of the annulus, the circumference of the inner annulus are given,
    • Inner annulus radius formula is r₂ = C₂ / 2π
    • The inner annulus area formula is A₂ = πr₂²
    • Outer annulus area formula is A₁ = A0 + A₂
    • Outer annulus radius formula is r₁ = √(A₁ / π )
    • The outer annulus circumference formula is C₁ = 2πr₁
  • If the area of annulus, area of the outer annulus is given,
    • Inner annulus area formula is A₂ = A₁ - A0
    • Outer annulus radius formula is r₁ = √(A₁ / π )
    • Inner annulus radius formula is r₂ = √(A₂ / π )
    • The outer annulus circumference formula is C₁ = 2πr₁
    • The inner annulus circumference formula is C₂ = 2πr₂
  • If the area of the inner annulus, area of the annulus are given,
    • Outer annulus area formula is A₁ = A0 + A₂
    • Outer annulus radius formula is r₁ = √(A₁ / π )
    • Inner annulus radius formula is r₂ = √(A₂ / π )
    • The outer annulus circumference formula is C₁ = 2πr₁
    • The inner annulus circumference formula is C₂ = 2πr₂

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 r₁ = 12 cm

The inner circle radius r₂ = 7 cm

Circumference of outer circle C₁ = 2πr₁

= 2 * 3.14 * 12

= 75.36

Circumference of inner circle C₂ = 2πr₂

= 2 * 3.14 * 7

= 43.96

Area of the outer circle A₁ = πr₁²

= 3.14 * 12²

= 3.14 * 12 * 12

= 452.16

Area of the inner circle A₂ = πr₂²

= 3.14 * 7²

= 3.14 * 7 * 7

= 153.86

Surface area of the annulus A0 = A₁ - A₂

= 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 r₁ = 8 m

Area of inner circle A₂ = 120 m²

Circumference of outer circle C₁ = 2πr₁

= 2 * 3.14 * 8

= 50.24

Area of the outer circle A₁ = πr₁²

= 3.14 * 8²

= 3.14 * 8 * 8

= 200.96

Radius of the inner circle r₂ = √(A₂ / π)

= √(120 / 3.14 )

= √38.21

= 6.18

Circumference of inner circle C₂ = 2πr₂

= 2 * 3.14 * 6.18

= 38.81

Surface area of the annulus A0 = A₁ - A₂

= 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))