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Annulus Calculator

 

r1 = outer radius
r2 = inner radius
C1 = outer circumference
C2 = inner circumference
A1 = area of circle of r1, area within outer circle
A2 = area of circle of r2, area within inner circle
A0 = shaded area, outer area minus inner area
A0 = A1 - A2
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 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 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, 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
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