Polygon Inradius Calculator

About this calculator

The inradius (apothem) of a regular polygon is the distance from its center to the midpoint of any side — equivalently, the radius of the largest circle that fits entirely inside the polygon. For a regular polygon with n sides of length s, it's calculated as r = s / (2 × tan(π/n)), which shrinks toward the circumradius as n grows large and the polygon approaches a circle.

The apothem shows up directly in the standard polygon area formula, Area = (1/2) × perimeter × apothem, which is why it matters in fields like machining and CNC programming (fitting a hex bolt head into a socket), carpentry and fabrication (cutting regular polygon panels or gazebo bases), and packaging design (nesting circular components inside hexagonal or octagonal trays).

This calculator takes the number of sides and side length of a regular polygon and returns its inradius, circumradius, and area in one step — useful for engineers, hobbyist woodworkers, and geometry students who need the apothem without re-deriving trigonometric identities each time.