Calculator Use

This calculator determines the area, circumference, and radii

of an annulus.

When any two measurements are known, the remaining quantities can be computed

automatically using the formulas below.

The shaded region of the annulus, represented by A₀, is found by

subtracting the area of the inner circle from the area of the outer circle:

A₀ = A₁ − A₂

Units:

Units of measurement (such as cm, m, ft) do not affect the formulas.

They simply express the scale of the result: length (unit),

area (unit²), or volume (unit³).

Annulus Formulas

The following formulas express the circumference and area of each circle in

terms of radius r and π.

Outer circumference:

C₁ = 2π r₁

Inner circumference:

C₂ = 2π r₂

Area enclosed by the outer circle:

A₁ = π r₁²

Area enclosed by the inner circle:

A₂ = π r₂²

Area of the annulus (shaded region):

A₀ = A₁ − A₂

= π(r₁² − r₂²)

Calculation Sets

The next sections show how to compute unknown values using different pairs of known inputs.

1 Given r₁ and r₂

• C₁ = 2π r₁
• C₂ = 2π r₂
• A₁ = π r₁²
• A₂ = π r₂²
• A₀ = A₁ − A₂

2 Given r₁ and C₂

• r₂ = C₂ / (2π)
• C₁ = 2π r₁
• A₁ = π r₁²
• A₂ = π r₂²
• A₀ = A₁ − A₂

3 Given r₁ and A₂

• r₂ = √(A₂ / π)
• C₁ = 2π r₁
• C₂ = 2π r₂
• A₁ = π r₁²
• A₀ = A₁ − A₂

4 Given r₂ and C₁

• r₁ = C₁ / (2π)
• C₂ = 2π r₂
• A₁ = π r₁²
• A₂ = π r₂²
• A₀ = A₁ − A₂