Calculation of the area of the ring

A ring is a flat geometric figure bounded by two concentric circles. The area of the ring is defined as the difference between the areas of the circles of the inner and outer radius. The area of a ring can also be calculated by multiplying pi by the square of half the length of the largest segment inside the ring. This can be proved through the Pythagorean theorem.

Find the area of a ring through the outer and inner radii

Ring outer radius R
Ring inner radius r

Find the area of a ring through the outer and inner diameters

External diameter D
Inner diameter d

Ring areas, through the average radius and width of the ring

Ring width K
Average radius r

Formula for the area of a ring in terms of the outer and inner radii: S = π (R² – r²)

Formula of ring area in terms of outer and inner diameters: S = π / 4 (D² – d²)

Formula for the area of a ring in terms of the average radius and width: S = 2πrk