Side-count closed forms
Regular polygon geometry
Inputs
Integer count for a regular convex polygon, at least 3.
Nominal equal side length of the regular polygon.
Results
Perimeter
120
Apothem
17.321
Circumradius
20
Each interior angle
120
Regular-polygon areaA
1,039.2
P = ns; a = s/[2 tan(π/n)]; R = s/[2 sin(π/n)]; α = (n−2)180°/n; A = aP/2
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Section geometry · Right-triangle frame · 3D coordinate span · Cylinder geometry
Method
Formula, when it applies, and when it does not
Calculate regular-polygon perimeter, apothem, circumradius, interior angle, and area from a side count and side length.
P = ns; a = s/[2 tan(π/n)]; R = s/[2 sin(π/n)]; α = (n−2)180°/n; A = aP/2
When
- Regular convex polygon
- Equal sides and angles
- Planar Euclidean geometry
- Nominal dimensions
Don’t
- This is planar regular-polygon closed-form geometry: every side and every interior angle are assumed equal. It does not calculate irregular polygons, tolerance zones, CAD/CAM geometry, feature position, material area allowance, manufacturability, structural response, or drawing compliance.
Elementary geometry — standard results