# Annulus - Calculator given value:
= =
calculated values:

This calculator can be used to calculate the area, perimeter and width of an annulus.

## Formulas Area
A = π ∙ (R² − r²)
A =
 π 4
∙ (D² − d²)
Perimeter
P = 2 ∙ π ∙ (R + r)
P = π ∙ (D + d)
Width
w = R − r
w =
 D − d 2

## What is an annulus?

An annulus is the area between 2 circle lines whose circles have different radii but the same center. ## Area of an annulus

To calculate the area of an annulus, you can subtract the area of the inner circle from the area of the outer circle. The area of an annulus is calculated by squaring the radius and multiplying the result by π. If R is the radius of the outer circle and r is the radius of the inner circle, then the area of the annulus can be calculated as follows:

A = (π ∙ R²) − (π ∙ r²)

This can be further simplified by factoring out π:

A = π ∙ (R² − r²)

### Calculation with diameters:

If you want to calculate the area of an annulus with the help of the diameter, then you square the diameter, multiply the result by π and divide the result of the multiplication by 4. If D is the diameter of the outer circle and d is the diameter of the inner circle, then the area of the annulus is calculated as follows:

A = (
 1 4
∙ π ∙ D²)(
 1 4
∙ π ∙ d²)

 π 4
can still be factored out. Then you get:

A =
 π 4
∙ (D² − d²)

Example:

The outer circle of an annulus has a radius of 4 cm ( resp. a diameter of 8 cm) and the inner circle has a radius of 2 cm ( resp. a diameter of 4 cm). The area of the annulus is to be calculated: A = π ∙ (R² − r²) = π ∙ ((4 cm)² − (2 cm)²) = π ∙ (16 cm² − 4 cm²) = π ∙ 12 cm² ≈ 37.69911 cm²

with diameters: A=
 π 4
∙ (D² − d²)
=
 π 4
∙ ((8 cm)² − (4 cm)²)
=
 π 4
∙ (64 cm² − 16 cm²)
=
 π 4
∙ 48 cm²
=π ∙ 12 cm²
37.69911 cm²

## Width of an annulus

### Width of annulus with radii:

If you draw in the radius of the outer circle, then the radius can be divided into 2 line segments. One line segment runs from the center of the two circles to the circle line of the inner circle. This is the radius of the inner circle. The other line segment runs from the circle line of the inner circle to the circle line of the outer circle. This line segment is the width of the annulus. The width of the annulus can be calculated by subtracting the radius of the inner circle from the radius of the outer circle.

w = R − r

### Width of annulus with diameters:

If you draw in the diameter of the outer circle, then this can be divided into 3 line segments. The middle line segment runs between the two intersections with the inner circle line and is the diameter of the inner circle. The two outer line segments run from the inner circle line to the outer circle line. These line segments are each the width of the annulus. If you want to calculate the width of the annulus using the diameters, subtract the diameter of the inner circle from the diameter of the outer circle and divide the result by 2.

w =
 D − d 2

Example:

The outer circle of an annulus has a radius of 4 cm ( resp. a diameter of 8 cm) and the inner circle has a radius of 2 cm ( resp. a diameter of 4 cm). The width of the annulus is to be calculated: w = R − r = 4 cm − 2 cm = 2 cm

with diameters: w=
 D − d 2
=
 8 cm − 4 cm 2
=
 4 cm 2
=2 cm

## Perimeter of an annulus

The perimeter of an annulus is calculated by adding the perimeter of the circle of the outer circle line and the perimeter of the circle of the inner circle line.

The perimeter of a circle is calculated with the formula: 2 ∙ π ∙ radius

Thus, for the perimeter of the annulus, if R is the radius of the outer circle and r is the radius of the inner circle, holds:

P = (2 ∙ π ∙ R) + (2 ∙ π ∙ r)

2 ∙ π can be factored out. Then you get:

P = 2 ∙ π ∙ (R + r)

### Calculate perimeter with diameters:

If you want to calculate the perimeter of a circle with the help of the diameter, then you can use the following formula: π ∙ diameter

Thus, for the perimeter of the annulus, if D is the diameter of the outer circle and d is the diameter of the inner circle, holds:

P = (π ∙ D) + (π ∙ d)

π can be factored out. Then you get:

P = π ∙ (D + d)

Example:

The outer circle of an annulus has a radius of 4 cm ( resp. a diameter of 8 cm) and the inner circle has a radius of 2 cm ( resp. a diameter of 4 cm). The perimeter of the annulus is to be calculated: