innerradius

Inner radius refers to the distance from the center of a circle to the inner boundary of a ring-shaped region. In geometry, an annulus is the area between two concentric circles with radii r and R, where R is the outer radius and r is the inner radius (R > r).

In mathematical terms, the area of an annulus is A = π(R^2 − r^2). The outer boundary has circumference 2πR, and the inner boundary has circumference 2πr. The inner radius is a key parameter in problems involving washers, rings, or hollowing a disk, and it determines the size of the central hole.

In practical applications, inner radius is commonly encountered in data visualization and graphics. In donut charts, the innerRadius controls the size of the hole in the center of the chart; it is often expressed as a fraction of the outer radius. For example, innerRadius = 0 yields a full disk, while innerRadius close to 1 produces a thin ring. In vector graphics and charting libraries, innerRadius may be specified directly in length units or as a normalized fraction of the outer radius.

Edge cases include r = 0, which produces a solid circle, and r ≥ R, which results in a degenerate shape with zero or negative area. The inner radius is always nonnegative and must be strictly less than the outer radius to form a true annulus.

See also: annulus, ring, donut chart, washer, concentric circles.