HomeCalculatorsMathGeometryRegular Polygon Calculator
Math calculator

Regular Polygon Calculator

Regular n-gon A = (n s²)/(4 tan(π/n)) for integer n≥3. Same engine as Plane Geometry. Not a triangle solver. Not CAS. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 25/25 tests · Production surface contract 3/3 · v1.3.0
Input interpretation
Enter values to calculate.
Result
—
Model
Regular n-gon area, perimeter, apothem, and interior angle.
Scope
Euclidean plane
Verification
Engine tested · 25/25 tests · Production surface contract 3/3 · Specification checked · v1.3.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
9 golden · 5 boundary · 11 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.3.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

AreaA = (n s²) / (4 tan(π/n))
Interior((n − 2) / n) × 180°
iSame engine as /plane-geometry. Equilateral triangle is n=3 here; the general triangle solver stays /triangle-solver. Not a second engine.

How to use

1

Enter n and s

n must be an integer ≥ 3. n = 6, s = 1 is the unit hexagon.

2

Read A, P, and the interior angle

A regular hexagon with s=1 has P=6 and interior 120°.

Example calculations

Common configurations with formula and result.

ϟ

Hexagon

n = 6, s = 1

A = 3√3/2
P=6, 120°
ϟ

Equilateral triangle

n = 3, s = 2

A = √3
interior 60°

Regular Polygon calculator specification

Version 1.3.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A regular n-gon with integer n≥3 and side s>0 has area (n s²)/(4 tan(π/n)), perimeter n s, interior angle ((n−2)/n)×180°, and apothem s/(2 tan(π/n)). This page is mode=regular_polygon on math.geometry.plane. Not a triangle solver. Not CAS.
What it calculates
Regular n-gon area, perimeter, apothem, and interior angle.
Inputs
  • n
  • s
Outputs
  • area
  • perimeter
  • apothem
  • interior_deg
Formula
A = (n s²)/(4 tan(π/n)), P = n s
Assumptions
  • Euclidean plane
  • Integer n ≥ 3
  • Not a triangle solver
  • Not CAS
Units
  • length (consistent units)
  • area (length²)
  • degrees
Boundary conditions
  • s ≤ 0 → VALUE_MUST_BE_POSITIVE
  • n < 3 or non-integer n → INVALID_INPUT
  • unknown mode → INVALID_MODE
Example
n=6 s=1 → P=6, interior=120°
Validation cases

2 published on this page · 25/25 tests · Production surface contract 3/3 · View evidence

  • n=6 s=1 → P=6 interior=120°
  • n=3 s=2 → interior=60°
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.3.0

Other calculators in this family: Angle Between Lines Calculator, Circle Calculator, Cone Calculator, Conic Section Calculator, Coordinate Geometry Calculator, Cross Product Calculator, Cylinder Calculator, Dot Product Calculator . Explore all Geometry.

→ Angle Between Lines Calculator Acute angle between two plane lines, each given by two points. Parallel is 0°. Perpendicular is 90°. Degenerate points are invalid. Same engine as Coordinate Geometry. Not a second engine. Not CAS. Runs locally. › → Circle Calculator Compute diameter, circumference, and area from r, or arc and sector from a central angle. Not the Pythagorean page. Runs locally. › → Cone Calculator Right circular cone V = (1/3)πr²h and slant l = √(r²+h²). Same engine as Solid Geometry. Not ISO 5167-5. Not CAS. Runs locally. › → Conic Section Calculator Axis-aligned ellipse, parabola, and hyperbola in standard form. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page. Not coordinate geometry. Not CAS. Runs locally. › → Coordinate Geometry Calculator Distance, midpoint, and slope of two points in the plane. Line through two points is /line-equation. Point-to-line distance is /point-line-distance. Intersection is /line-intersection. Angle is /angle-between-lines. Not the Pythagorean-only page. Runs locally. › → Cross Product Calculator Vector product u × v in R³. 2-D uses uz = vz = 0. Same engine as Vector. Not a matrix. Not CAS. Runs locally. › → Cylinder Calculator Right circular cylinder V = πr²h and A = 2πr(r+h). Same engine as Solid Geometry. Not CAS. Runs locally. › → Dot Product Calculator Scalar product u · v = ux vx + uy vy + uz vz. Same engine as Vector. Not a matrix. Not CAS. Runs locally. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this a second plane engine?

No. It is mode=regular_polygon on math.geometry.plane, the same engine as /calc/math/plane-geometry.

Is n=3 the triangle solver?

No. n=3 is the equilateral case on this engine. SSS/SAS/ASA stay on /calc/math/triangle-solver.

Where does this run?

Locally in the browser by default. REST and MCP call the same plane-geometry engine.