Solve a regular polygon from the number of sides plus any one known size — side, perimeter, area, apothem, circumradius, across flats, or across corners — with a live diagram and exact derived geometry.
Choose the side count, then give the one measurement you actually know. Everything else updates instantly.
Keep a few comparisons while you work. These snapshots are not written to localStorage.
Calculations run locally in your browser. The unit selector labels the result; it does not change the underlying geometry.
For a regular n-gon, the side count plus any one independent size fixes the scale. That is why this solver accepts side, perimeter, area, apothem, circumradius, or the corresponding circle diameters.
The apothem reaches the midpoint of a side and equals the incircle radius. The circumradius reaches a vertex. Mixing these two radii is a common source of incorrect area calculations.
For even-sided polygons these match practical opposite-face and opposite-vertex measurements used for square, hex and octagonal stock. For odd n the page deliberately labels them as circle diameters rather than pretending opposite faces exist.
Connect the center to every vertex. The polygon becomes n congruent triangles, each with base s and height equal to the apothem, so total area is one-half × perimeter × apothem.
Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.
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