# Annulus Calculator

Determine the properties of annuli (ring-shaped regions) with our Annulus Calculator.

r_{1} = | |

r_{2} = | |

Units: | |

C_{1} = | 0 |

C_{2} = | 0 |

A_{1} = | 0 |

A_{2} = | 0 |

A_{0} = | 0 |

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An annulus is a two-dimensional geometric shape that resembles a ring or a circular donut. It is created by removing a smaller circle from a larger one. The annulus consists of two concentric circles, where one is the outer boundary, and the other is the inner boundary.

r1 = outer radius

r2 = inner radius

C1 = outer circumference

C2 = inner circumference

A1 = area of circle of r1

A2 = area of circle of r2

A0 = shaded area

The online annuluses calculator to find the area, circumference, and radius of an annulus. When you know two known variables, then select from the droplist and calculate the other 5 unknowns.

## Annulus Formulas

**Given r1 and C2:**

r2 = C2 / 2π

C1 = 2πr1

A1 = πr12

A2 = πr22

A0 = A1 – A2.

**Given r1 and A2:**

r2 = √(A2 / π)

C1 = 2πr1

C1 = 2πr2

A1 = πr12

A0 = A1 – A2.

**Given C1 and C2:**

r1 = C1 / 2π

r2 = C1 / 2π

A1 = πr12

A2 = πr22

A0 = A1 – A2.

**Given r2 and A1:**

r1 = √(A1 / π)

C1 = 2πr1

C2 = 2πr2

A2 = πr22

A0 = A1 – A2.

**Given A1 and A2:**

r1 = √(A1 / π)

r2 = √(A2 / π)

C1 = 2πr1

C2 = 2πr2

A0 = A1 – A2.

**Given r2 and A0:**

C2 = 2πr2

A2 = πr22

A1 = A0 + A2

r1 = √(A1 / π)

C1 = 2πr2.

**Given C2 and A0:**

r2 = C2 / 2π

A2 = πr22

A1 = A0 + A2

r1 = √(A1 / π)

C1 = 2πr1.

**Given A2 and A0:**

A1 = A0 + A2

r1 = √(A1 / π)

r2 = √(A2 / π)

C1 = 2πr1

C2 = 2πr2.

**Given r1 and r2:**

C1 = 2πr1

C2 = 2πr2

A1 = πr12

A2 = πr22

A0 = A1 – A2.

**Given r2 and C1:**

r1 = C1 / 2π

C2 = 2πr2

A1 = πr12

A2 = πr22

A0 = A1 – A2.

**Given C1 and A2:**

r1 = C1 / 2π

r2 = √(A2 / π)

C2 = 2πr2

A1 = πr12

A0 = A1 – A2.

**Given C2 and A1:**

r1 = √(A1 / π)

r2 = C2 / 2π

C1 = 2πr1

A2 = πr22

A0 = A1 – A2.

**Given r1 and A0:**

C1 = 2πr1

A1 = πr12

A2 = A1 – A0

r2 = √(A2 / π)

C2 = 2πr2.

**Given C1 and A0:**

r1 = C1 / 2π

A1 = πr12

A2 = A1 – A0

r2 = √(A2 / π)

C2 = 2πr2.

**Given A1 and A0:**

A2 = A1 – A0

r1 = √(A1 / π)

r2 = √(A2 / π)

C1 = 2πr1

C2 = 2πr2.

The annulus is a geometric shape characterized by its concentric circles and the space between them. It finds applications in various real-world scenarios, from engineering to art and design. By understanding its properties and calculations, you can appreciate the elegance and versatility of this geometric figure.