Annulus Calculator
Annulus Shape
r_{1} = outer radius
r_{2} = inner radius
C_{1} = outer circumference
C_{2} = inner circumference
A_{1} = area of circle of r_{1}, area within outer circle
A_{2} = area of circle of r_{2}, area within inner circle
A_{0} = shaded area, outer area minus inner area
A_{0} = A_{1}  A_{2}
π = pi = 3.1415926535898
√ = square root
Calculator Use
This online calculator will find the area, circumference and radii of an annulus. With any 2 known variables you can calculate the other 5 unknowns. Use the following formulas and sets of equations below to calculate measures of an annulus.
Area of the annulus between r_{1} and r_{2}, the shaded area, is the area contained by the outer circle minus the area contained by the inner circle or A_{0} = A_{1}  A_{2}. You will need to know 2 elements in order to calculate the remaining 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, ft^{2} or ft^{3}. Any other base unit can be substituted.
Annulus Formulas in terms of radius r and π
Outer circumference of an annulus:
C_{1} = 2πr_{1}
Inner circumference of an annulus:
C_{2} = 2πr_{2}
Surface area of the space enclosed by the outer circle
A_{1} = πr_{1}^{2}
Surface area of the space enclosed by the inner circle
A_{2} = πr_{2}^{2}
Surface area of the annulus (the gray shaded area)
A_{0} = A_{1}  A_{2}
= (πr_{1}^{2})  (πr_{2}^{2})
= π(r_{1}^{2}  r_{2}^{2})
Annulus Calculations:
The following are the sets of formulas we used in our calculations:

Calculate C_{1}, C_{2}, A_{1}, A_{2}, A_{0}  Given r_{1}, r_{2}
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. C_{1} = 2πr_{1}
 C_{2} = 2πr_{2}
 A_{1} = πr_{1}^{2}
 A_{2} = πr_{2}^{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{2}, C_{1}, A_{1}, A_{2}, A_{0}  Given r_{1}, C_{2}
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. r_{2} = C_{2} / 2π
 C_{1} = 2πr_{1}
 A_{1} = πr_{1}^{2}
 A_{2} = πr_{2}^{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{2}, C_{1}, C_{2}, A_{1}, A_{0}  Given r_{1}, A_{2}
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. r_{2} = √(A_{2} / π )
 C_{1} = 2πr_{1}
 C_{2} = 2πr_{2}
 A_{1} = πr_{1}^{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{1}, C_{2}, A_{1}, A_{2}, A_{0}  Given C_{1}, r_{2}
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. r_{1} = C_{1} / 2π
 C_{2} = 2πr_{2}
 A_{1} = πr_{1}^{2}
 A_{2} = πr_{2}^{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{1}, r_{2}, A_{1}, A_{2}, A_{0}  Given C_{1}, C_{2}
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. r_{1} = C_{1} / 2π
 r_{2} = C_{2} / 2π
 A_{1} = πr_{1}^{2}
 A_{2} = πr_{2}^{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{1}, r_{2}, C_{2}, A_{1}, A_{0}  Given C_{1}, A_{2}
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. r_{1} = C_{1} / 2π
 r_{2} = √(A_{2} / π )
 C_{2} = 2πr_{2}
 A_{1} = πr_{1}^{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{1}, C_{1}, C_{2}, A_{2}, A_{0}  Given A_{1}, r_{2}
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. r_{1} = √(A_{1} / π )
 C_{1} = 2πr_{1}
 C_{2} = 2πr_{2}
 A_{2} = πr_{2}^{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{1}, r_{2}, C_{1}, A_{2}, A_{0}  Given A_{1}, C_{2}
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. r_{1} = √(A_{1} / π )
 r_{2} = C_{2} / 2π
 C_{1} = 2πr_{1}
 A_{2} = πr_{2}^{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{1}, r_{2}, C_{1}, C_{2}, A_{0}  Given A_{1}, A_{2}
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. r_{1} = √(A_{1} / π )
 r_{2} = √(A_{2} / π )
 C_{1} = 2πr_{1}
 C_{2} = 2πr_{2}
 A_{0} = A_{1}  A_{2}

Calculate r_{2}, C_{1}, C_{2}, A_{2}, A_{0}  Given A_{0}, r_{1}
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. C_{1} = 2πr_{1}
 A_{1} = πr_{1}^{2}
 A_{2} = A_{1}  A_{0}
 r_{2} = √(A_{2} / π )
 C_{2} = 2πr_{2}

Calculate r_{1}, C_{1}, C_{2}, A_{1}, A_{2}  Given A_{0}, r_{2}
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. C_{2} = 2πr_{2}
 A_{2} = πr_{2}^{2}
 A_{1} = A_{0} + A_{2}
 r_{1} = √(A_{1} / π )
 C_{1} = 2πr_{1}

Calculate r_{1}, r_{2}, C_{2}, A_{1}, A_{2}  Given A_{0}, C_{1}
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. r_{1} = C_{1} / 2π
 A_{1} = πr_{1}^{2}
 A_{2} = A_{1}  A_{0}
 r_{2} = √(A_{2} / π )
 C_{2} = 2πr_{2}

Calculate r_{1}, r_{2}, C_{1}, A_{1}, A_{2}  Given A_{0}, C_{2}
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. r_{2} = C_{2} / 2π
 A_{2} = πr_{2}^{2}
 A_{1} = A_{0} + A_{2}
 r_{1} = √(A_{1} / π )
 C_{1} = 2πr_{1}

Calculate r_{1}, r_{2}, C_{1}, C_{2}, A_{2}  Given A_{0}, A_{1}
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. A_{2} = A_{1}  A_{0}
 r_{1} = √(A_{1} / π )
 r_{2} = √(A_{2} / π )
 C_{1} = 2πr_{1}
 C_{2} = 2πr_{2}

Calculate r_{1}, r_{2}, C_{1}, C_{2}, A_{1}  Given A_{0}, A_{2}
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. A_{1} = A_{0} + A_{2}
 r_{1} = √(A_{1} / π )
 r_{2} = √(A_{2} / π )
 C_{1} = 2πr_{1}
 C_{2} = 2πr_{2}
Cite this content, page or calculator as:
Furey, Edward "Annulus Calculator" at https://www.calculatorsoup.com/calculators/geometryplane/annulus.php from CalculatorSoup, https://www.calculatorsoup.com  Online Calculators
Last updated: September 16, 2023