# Regular Polygon Area Calculator

> Area, perimeter, apothem and angles of any regular polygon — pentagon, hexagon, octagon and more.

Page: https://freecalculator.tech/tools/regular-polygon-area-calculator
Last reviewed: 2026-11-03

## Formula

A = n s² ÷ (4 tan(π/n)); apothem = s ÷ (2 tan(π/n)); circumradius = s ÷ (2 sin(π/n)); interior angle = (n − 2) × 180° ÷ n.

- Source: Wolfram MathWorld, Regular Polygon.
- Regular means every side and every angle is equal.
- A = n s² ÷ (4 tan(π/n)); apothem = s ÷ (2 tan(π/n)); circumradius = s ÷ (2 sin(π/n)); interior angle = (n − 2) × 180° ÷ n.
- Inputs used: Number of sides n, Side length s, Unit (labels only — no conversion).

## Inputs

- Number of sides n
- Side length s
- Unit (labels only — no conversion)

## Worked example: Regular hexagon, side 2

6 × 2² ÷ (4 tan 30°) ≈ 10.3923 cm².
1. tan(π/6) ≈ 0.57735.
2. Area = 24 ÷ (4 × 0.57735) ≈ 10.3923 cm².

## Common questions

### Does this work for irregular shapes?

No. All sides and angles must be equal.

### What is the apothem?

The distance from the centre to the midpoint of a side; area also equals perimeter × apothem ÷ 2.

### Which n gives an octagon?

Enter 8. A pentagon is 5 and a hexagon is 6.

### How do I use the Regular Polygon Area Calculator?

Enter the required values for Number of sides n, Side length s, Unit (labels only — no conversion). The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Regular Polygon Area Calculator use?

A = n s² ÷ (4 tan(π/n)); apothem = s ÷ (2 tan(π/n)); circumradius = s ÷ (2 sin(π/n)); interior angle = (n − 2) × 180° ÷ n. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

### Can the Regular Polygon Area Calculator be used for exact decisions?

Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.

## Limitations and assumptions

- Regular convex polygons only.
- Star polygons are not supported.
- Exact mathematical relationships, rounded for display. Check units and rounding before using a result in graded, engineering or financial work.
- The result depends on the values you enter for this regular polygon area calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- Wolfram MathWorld — https://mathworld.wolfram.com/RegularPolygon.html

## Cite this page

- APA: Free Calculator. (2026, November 3). Regular Polygon Area Calculator. https://freecalculator.tech/tools/regular-polygon-area-calculator
- MLA: "Regular Polygon Area Calculator." Free Calculator, 3 Nov. 2026, https://freecalculator.tech/tools/regular-polygon-area-calculator.
- Link: Regular Polygon Area Calculator — Free Calculator, https://freecalculator.tech/tools/regular-polygon-area-calculator