**Instructions:**

- Enter the outer and inner radii for the annulus.
- Select the unit for area and circumference calculation.
- Click "Calculate" to calculate the attributes of the annulus.
- View the results below, including detailed calculations.
- Use the chart to visualize the annulus.
- Copy the results or clear them as needed.
- Check the calculation history for previous entries.

**Calculation Details:**

**Area:** The area of the annulus is calculated using the formula A = π(R2^2 - R1^2).

**Inner Circumference:** The inner circumference is calculated using the formula C = 2πR1.

**Outer Circumference:** The outer circumference is calculated using the formula C = 2πR2.

**Inner Circle Area:** The area of the inner circle is calculated using the formula A = πR1^2.

**Outer Circle Area:** The area of the outer circle is calculated using the formula A = πR2^2.

**Calculation History:**

An annulus is a geometric shape that is formed by two concentric circles. The Annulus Calculator is an online tool that helps you calculate the area, circumference, and radii of an annulus. With any two known variables, you can calculate the other five unknowns.

## Concepts

An annulus is a two-dimensional shape that consists of two concentric circles. The outer circle has a larger radius than the inner circle. The area of an annulus is the difference between the area of the outer circle and the area of the inner circle. The circumference of an annulus is the sum of the circumference of the outer circle and the circumference of the inner circle.

## Formulae

The following formulae are used to calculate measures of an annulus:

- Outer circumference of an annulus:
`C1 = 2πr1`

- Inner circumference of an annulus:
`C2 = 2πr2`

- Surface area of the space enclosed by the outer circle:
`A1 = πr1^2`

- Surface area of the space enclosed by the inner circle:
`A2 = πr2^2`

- Surface area of the annulus (the gray shaded area):
`A0 = A1 - A2 = π(r1^2 - r2^2)`

## Benefits

The Annulus Calculator provides a quick and easy way to calculate measures of an annulus. It can be used in various fields such as engineering, architecture, and mathematics. It saves time and effort by eliminating manual calculations.

## Interesting Facts

- The word “annulus” comes from Latin and means “ring”.
- The area of an annulus can also be calculated using Green’s theorem.
- The Annulus Calculator can be used to calculate measures of other shapes such as torus and circular sector.

## Use Cases

The Annulus Calculator can be used in various fields such as:

- Engineering: It can be used to calculate measures of annular seals, gaskets, and bearings.
- Architecture: It can be used to calculate measures of circular windows, doors, and skylights.
- Mathematics: It can be used to teach students about geometric shapes and their properties.

**References**

- Kostov, Vasil. “On the Area Formula for Annuli.” Journal of Geometry 107, no. 1 (2016): 119-26. https://doi.org/10.1007/s00022-015-0297-y