Online calculator to calculate the enclosed area \( A \), the inner radius \( R_2 \), and the outer radius \( R_1 \) of a circular ring when any two parameters are known.
Figure 1. Circular ring (annulus) with outer radius R₁ and inner radius R₂
About the Circular Ring (Annulus)
The area \( A \) of a circular ring bounded by two concentric circles with outer radius \( R_1 \) and inner radius \( R_2 \) (where \( R_1 \ge R_2 \)) is given by:
\[ A = \pi (R_1^2 - R_2^2) \]
This formula can be rearranged to solve for any unknown if the other two are known:
Given \( R_1 \) and \( R_2 \): \( A = \pi (R_1^2 - R_2^2) \) for \( R_1 \ge R_2 \)
Given \( A \) and \( R_1 \): \( R_2 = \sqrt{R_1^2 - \dfrac{A}{\pi}} \) for \( R_1 \ge \sqrt{\dfrac{A}{\pi}} \)
Given \( A \) and \( R_2 \): \( R_1 = \sqrt{R_2^2 + \dfrac{A}{\pi}} \)
💡 How to use: Enter any two of the three values (R₁, R₂, Area). Leave the third field empty. The calculator will compute the missing value for you. All values should use the same unit system.
Annulus Calculator
Enter any two values. The third will be calculated automatically.
