Circular Ring Area

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Circular Ring Area Calculation:

  •  R =

    Radius of the outside circle, the larger radius

  •  r =

    Radius of the inside circle, the smaller radius

  •  A =

    Area between the inside and outside circle, known as an annulus

  •

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Circular Ring Area Formula

Circular ring area is the area between two concentric circles, this area is also known as an annulus. The area between the two concentric circles can be calculated using the radius of the outer circle, denoted as R, R1 or r1, and the radius of the inner circle, usually denoted r or r2.

A = π(R12 - r22)

Circular Ring Formula
Area of a Circular Ring or Annulus Calculation

Circular Ring Area Variables

Area can be calculed by knowing the radii of the two concentric circles.

Radius 1 (R1)
Radius of the larger most outer circle. The larger circle must be radius 1 for the formula to work.
Radius 2 (r2)
Radius of the smaller, inner, circle. The radius of the smalled circle must be subtracted from the radius of the larger circle, the two radii are not interchangeable in the formula.
Area (A)
Area between the two concentric circles, also known as the annulus. In square units.

Circular Ring Area Solution

How do we calculate the area of a circular ring with an outer radius of 3 and an inner radius of 2?

  • A = π(R12 - r22)
  • Formula to use for calculating the area
  • A = π(32 - 22)
  • Substitute in the radii values
  • A = π(9 - 4)
  • Calculate the powers
  • A = π(5)
  • Calculate subtraction inside brackets
  • A = 3.14159(5)
  • Use a value of 3.14159 for π
  • A = 15.70795
  • Final multiplication and result
  • 15.70795 square units

The area between concentric circules a radius of 3 and a radius of 2 is 15.70795 square units, using an approximation of 3.14159 as π.

Circular Ring Area Example

What is the area of the annulus between a pipe with the radius of 10.5 inches and a pipe of 6 inches? Assume the pipes have no thickness, or we are measuring from outside the smaller pipe to inside the larger pipe.

  • A = π(R12 - r22)
  • A = π(10.52 - 62)
  • A = π(110.25 - 36)
  • A = 3.14159(74.25)
  • 233.2630575

An outer pipe with a radius of 10.5 inches and an inner pipe with a radius of 6 inches has an annular space of about 233.26 square inches.

Square Inches Converter

Convert square inches to other units

Circular Ring Formula