Annulus Calculator

An Annulus is a ring shaped object (the area between two concentric circles). Enter the dimensions of the outer and inner circles to calculate the annulus, view further details and information on Annulus Calculations below the Annulus Calculator. Enter the Annulus radius or diameter values for the inner and outer circle to calculate the area of an annulus and associated circumferences.

Annulus Calculator rules:

  1. The inner radius cannot be bigger than or equal to the outer radius
  2. The inner diameter cannot be bigger than or equal to the outer diameter
Annulus Calculator
Annulus Inner Dimensions
Annulus Outer Dimensions
Results (detailed calculations and formula below)
Annulus Outer Circumference C1 =
Annulus Inner Circumference C2 =
Annulus Outer Area A1 =
Annulus Inner Area A2 =
Annulus Area A =
Annulus Width W =
Annulus Outer Circumference Calculations
C1 = 2π × r1
C1 = (2 × ) ×
C1 = ×
C1 =
Annulus Inner Circumference Calculations
C2 = 2π × r1
C2 = (2 × ) ×
C2 = ×
C2 =
Annulus Outer Area Calculations
A1 = π × r12
A1 = × 2
A1 = ×
A1 =
Annulus Inner Area Calculations
A2 = π × r22
A2 = × 2
A2 = ×
A2 =
Annulus Area Calculations
A = A1 - A2
A = -
A =
Annulus Width Calculations
W = D1 - D2/2
W = - /2
W = /2
W =
Calculator Input Values
Annulus Inner Diameter D2 =
Annulus Inner Radius r2 =
Annulus Outer Diameter D1 =
Annulus Outer Radius r1 =
Archimedes Constant (π) =
Unit of measurement =
Annulus Calculator: An Annulus is a ring shaped object (the area between two concentric circles). This image shows an annulus shape with associated calculations used by the Annulus Calculator

Notes on the Annulus Calculator

  • The Radius is the distance between the centre of a circle and its edge. r1 = Outside radius and r2 = Inside radius
  • The Circumference is the distance around a circle. C1 represents the outer circle of the Annulus and C2 represents the inner circle of the annulas
  • The Area of an Annulus is calculated by subtracting the area based on the outside diameter from the area based on the inside diameter.
  • The width (W) of an Annulus is calculated by dividing the difference between the outside and inside diameters by two.

Online Annulus Calculator: No more Tedious Manual Calculations & The Math Errors That Follow

We know circles, and we know concentric circles, right? And then we have a ring, a solid circular band. Did you know that there is mathematical term for the band of a ring? It's called an annulus.

Image showing the properties of an annulas

As shown in the image above, the red region between the outer radius (R, also marked as Ro or R1) and the inner radius (r, also marked as Ri or R2) is an annulus. If you were asked to find the thickness of a ring, you'll be technically measuring the thickness or the height of the annulus.

The concentric rings of Saturn are annular; a metal washer is an annulus, a perfect circular wedding band is an annulus. The tires of a car, circular watch dial, we see more annulus in our daily life than we notice.

What are the Properties of an Annulus?

The outer and inner circles of an annulus have a common center, i.e. they are concentric circles. Apart from that, annulus shares its properties with a circle.

How to Calculate the Area of an Annulus?

Since an annulus is the region between two concentric circles, its area can be calculated by subtracting the area of inner circle from the area of the outer circle.

Area of Annulus = πR² - πr²

For example, if a ring has an outer radius of 3cm and inner radius of 1cm, the area of the annulus will be:

π3² - π1² = π (9-1) = π(8) = 25.14cm²

The Annulus Calculator includes the following forumula

Annulas Diameter Formula

Radius x 2

Annulas Radius Formula

Diameter x 0.5

Annulas Circumference Formula

π x Diameter

Annulas Area Formula

(2 x π x radius of the outer circle) - (2 x π x radius of the inner circle)

PI is 3.141592654 (to 9 decimal places)

Why do I need an Annulus Calculator?

Calculations revolving around an annulus are not limited to calculating its area. Since the annulus is a circle with two radii, you also need to find the circumference of the band. Calculating all these measurements is easier said than done, especially when you are going to calculate the fractions. And even when you use a standard calculator, you'll be doing multiple calculations to find the area of the first circle, then move on to calculating the area of the second circle, and then subtract them. And this will only give you the area of the annulus, and that's it.

However, an annulus calculator saves you a lot of time and effort by giving you all the required information in a matter of few clicks. With the diameters or the radii entered into the calculator, you will be able to know the circumferences of the two concentric circles, their respective areas, and the area of the annulus as well as its width.

Calculating Annulus in Everyday Life

From making sturdy rings to manufacturing tires that stand the test of rough corners and harsh weather, annulus plays a vital role. Consider it this way: high profile tires have large annulus while low profile tires have small annulus. How much height a tire must have depends on its usage. From bicycles to bikes to cars to airplanes, tires are an integral part of every vehicle.

Also, if you are planning to install a circular pool in your backyard, the thickness of the walls determines how much water and use it can take. And it's not about the capacity alone. The thickness of the pool walls lets you figure out how much water pressure the pool can withstand. In case of circular washers, the width of annulus helps in identifying the right washer for the right nut and bolt.

We may not realize this often, but we come across annulus on a daily basis. The thing is, we don't always need to calculate its area. But when we do, we don't have to worry about doing all the mathematics manually, for there's an annulus calculator at our disposal, giving you accurate results quickly and effortlessly.

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