Annulus Calculator

Annulus Shape

r₁ = outer radius
r₂ = inner radius
C₁ = outer circumference
C₂ = inner circumference
A₀ = shaded area
A₁ = area of circle of r₁
A₂ = area of circle of r₂
π = pi = 3.14159
√ = square root

About this Calculator

Online calculator to find the area, circumference and radii of an annulus. With any 2 known variable you can calculate the other 5 unknowns. Use the following formulas and sets of equations below.

Area of the annulus between r₁ and r₂, the shaded area, is the area contained by the outer circle minus the area contained by the inner circle or A₀ = A₁ - A₂. You will need to know 2 items of information in order to calculate the remainder of variables.

* Units: Note that units of length are shown for convenience.  They do not affect the calculations.  The units are in place to give an indication of the order of the calculated results such as ft, ft² or ft³.  Any other base unit can be substituted.

Annulus Formulas in terms of radius r and π

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 = πr₁²

Surface area of the space enclosed by the inner circle

A₂ = πr₂²

Surface area of the annulus (the gray shaded area)

A₀ = A₁ - A₂
= (πr₁²) - (πr₂²)
= π(r₁² - r₂²)

Annulus Calculations:

The following are the sets of formulas we used in our calculations:

• Calculate C₁, C₂, A₁, A₂, A₀ | Given r₁, r₂
  Calculate outer circumference, inner circumference, area enclosed by the outer circle, area enclosed by the inner circle, area of the shaded region | Given outer radius, inner radius.
  • C₁ = 2πr₁
  • C₂ = 2πr₂
  • A₁ = πr₁²
  • A₂ = πr₂²
  • A₀ = A₁ - A₂
• Calculate r₂, C₁, A₁, A₂, A₀ | Given r₁, C₂
  Calculate inner radius, outer circumference, area enclosed by the outer circle, area enclosed by the inner circle, area of the shaded region | Given outer radius, inner circumference.
  • r₂ = C₂ / 2π
  • C₁ = 2πr₁
  • A₁ = πr₁²
  • A₂ = πr₂²
  • A₀ = A₁ - A₂
• Calculate r₂, C₁, C₂, A₁, A₀ | Given r₁, A₂
  Calculate inner radius, outer circumference, inner circumference, area enclosed by the outer circle, area of the shaded region | Given outer radius, area enclosed by the inner circle.
  • r₂ = √(A₂ / π )
  • C₁ = 2πr₁
  • C₂ = 2πr₂
  • A₁ = πr₁²
  • A₀ = A₁ - A₂
• Calculate r₁, C₂, A₁, A₂, A₀ | Given C₁, r₂
  Calculate outer radius, inner circumference, area enclosed by the outer circle, area enclosed by the inner circle, area of the shaded region | Given inner radius, outer circumference.
  • r₁ = C₁ / 2π
  • C₂ = 2πr₂
  • A₁ = πr₁²
  • A₂ = πr₂²
  • A₀ = A₁ - A₂
• Calculate r₁, r₂, A₁, A₂, A₀ | Given C₁, C₂
  Calculate outer radius, inner radius, area enclosed by the outer circle, area enclosed by the inner circle, area of the shaded region | Given outer circumference, inner circumference.
  • r₁ = C₁ / 2π
  • r₂ = C₂ / 2π
  • A₁ = πr₁²
  • A₂ = πr₂²
  • A₀ = A₁ - A₂
• Calculate r₁, r₂, C₂, A₁, A₀ | Given C₁, A₂
  Calculate outer radius, inner radius, inner circumference, area enclosed by the outer circle, area of the shaded region | Given outer circumference, area enclosed by the inner circle.
  • r₁ = C₁ / 2π
  • r₂ = √(A₂ / π )
  • C₂ = 2πr₂
  • A₁ = πr₁²
  • A₀ = A₁ - A₂
• Calculate r₁, C₁, C₂, A₂, A₀ | Given A₁, r₂
  Calculate outer radius, outer circumference, inner circumference, area enclosed by the inner circle, area of the shaded region | Given inner radius, area enclosed by the outer circle.
  • r₁ = √(A₁ / π )
  • C₁ = 2πr₁
  • C₂ = 2πr₂
  • A₂ = πr₂²
  • A₀ = A₁ - A₂
• Calculate r₁, r₂, C₁, A₂, A₀ | Given A₁, C₂
  Calculate outer radius, inner radius, outer circumference, area enclosed by the inner circle, area of the shaded region | Given inner circumference, area enclosed by the outer circle.
  • r₁ = √(A₁ / π )
  • r₂ = C₂ / 2π
  • C₁ = 2πr₁
  • A₂ = πr₂²
  • A₀ = A₁ - A₂
• Calculate r₁, r₂, C₁, C₂, A₀ | Given A₁, A₂
  Calculate outer radius, inner radius, outer circumference, inner circumference, area of the shaded region | Given area enclosed by the outer circle, area enclosed by the inner circle.
  • r₁ = √(A₁ / π )
  • r₂ = √(A₂ / π )
  • C₁ = 2πr₁
  • C₂ = 2πr₂
  • A₀ = A₁ - A₂
• Calculate r₂, C₁, C₂, A₂, A₀ | Given A₀, r₁
  Calculate inner radius, outer circumference, inner circumference, area enclosed by the outer circle, area enclosed by the inner circle | Given outer radius, area of the shaded region.
  • C₁ = 2πr₁
  • A₁ = πr₁²
  • A₂ = A₁ - A₀
  • r₂ = √(A₂ / π )
  • C₂ = 2πr₂
• Calculate r₁, C₁, C₂, A₁, A₂ | Given A₀, r₂
  Calculate outer radius, outer circumference, inner circumference, area enclosed by the outer circle, area enclosed by the inner circle | Given inner radius, area of the shaded region.
  • C₂ = 2πr₂
  • A₂ = πr₂²
  • A₁ = A₀ + A₂
  • r₁ = √(A₁ / π )
  • C₁ = 2πr₁
• Calculate r₁, r₂, C₂, A₁, A₂ | Given A₀, C₁
  Calculate outer radius, inner radius, inner circumference, area enclosed by the outer circle, area enclosed by the inner circle | Given outer circumference, area of the shaded region.
  • r₁ = C₁ / 2π
  • A₁ = πr₁²
  • A₂ = A₁ - A₀
  • r₂ = √(A₂ / π )
  • C₂ = 2πr₂
• Calculate r₁, r₂, C₁, A₁, A₂ | Given A₀, C₂
  Calculate outer radius, inner radius, outer circumference, area enclosed by the outer circle, area enclosed by the inner circle | Given inner circumference, area of the shaded region.
  • r₂ = C₂ / 2π
  • A₂ = πr₂²
  • A₁ = A₀ + A₂
  • r₁ = √(A₁ / π )
  • C₁ = 2πr₁
• Calculate r₁, r₂, C₁, C₂, A₂ | Given A₀, A₁
  Calculate outer radius, inner radius, outer circumference, inner circumference, area enclosed by the inner circle | Given area enclosed by the outer circle, area of the shaded region.
  • A₂ = A₁ - A₀
  • r₁ = √(A₁ / π )
  • r₂ = √(A₂ / π )
  • C₁ = 2πr₁
  • C₂ = 2πr₂
• Calculate r₁, r₂, C₁, C₂, A₁ | Given A₀, A₂
  Calculate outer radius, inner radius, outer circumference, inner circumference, area enclosed by the outer circle | Given area enclosed by the inner circle, area of the shaded region.
  • A₁ = A₀ + A₂
  • r₁ = √(A₁ / π )
  • r₂ = √(A₂ / π )
  • C₁ = 2πr₁
  • C₂ = 2πr₂