Regular Polygon Area Calculator
Compute area, perimeter, circumradius, and apothem for a regular polygon. Enter integer side count n and equal side length s. Irregular polygons are out of scope.
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How to find regular polygon area
- Enter the number of sides n as an integer from 3 to 1000. The default is a hexagon with n = 6.
- Enter the common side length s. The default side is 2.
- Read area from A = (n s²) / (4 tan(π/n)).
- Read perimeter as n × s, plus circumradius R and apothem for the same regular figure.
- Confirm every side and interior angle are equal. This page does not accept coordinate lists for irregular polygons.
Regular polygon area
Equal-sided, equal-angled n-gon from side length
| Area formula | A = (n s²) / (4 tan(π/n)) |
|---|---|
| Perimeter | P = n × s |
| Circumradius | R = s / (2 sin(π/n)) |
| Apothem | Distance from center to a side: s / (2 tan(π/n)) |
| Scope | Regular polygons only (equal sides and angles) |
| Default example | Regular hexagon, n = 6, s = 2 |
What a regular polygon is here
A regular polygon has equal sides and equal interior angles. Squares, equilateral triangles, and regular hexagons all fit. This page needs only the side count and one side length. It does not accept a list of unequal edge lengths.
How area, R, and apothem are formed
Area = (n s²) / (4 tan(π/n)). Perimeter = n s. Circumradius R = s / (2 sin(π/n)) reaches each vertex from the center. Apothem = s / (2 tan(π/n)) is the inradius to the middle of a side. Side count n must be an integer from 3 through 1000.
Why irregular polygons are excluded
Irregular polygons need vertex coordinates or a triangulation plan. The closed tan formula above assumes equal sides and a shared center. Feeding an average side length into this form for a skewed shape will misstate area.
Use cases
Honeycomb hex tiles, stop-sign octagons, and classroom regular n-gon drills. Floor plans with unequal walls need a survey or shoelace method, not this regular formula.
Limits
Regular only. No coordinate shoelace. No unit conversion. Non-integer n or n outside 3…1000 fails in the status line. See the disclaimer.