# Regular Polygon Calculator

URL: https://speedycalculator.com/calculators/math/regular-polygon/
Last updated: 2026-10-25

> The regular polygon calculator finds the area, perimeter, interior angle, apothem and circumradius of any regular polygon from the number of sides and the side length.

## Inputs

- Number of sides
- Side length (m, cm, mm, km, in, ft, yd, mi)

## Results

- Area
- Perimeter
- Interior angle
- Apothem (inradius)
- Circumradius

## Formula

```
Area = n s² ÷ (4 tan(π ÷ n))
Interior angle = (n − 2) × 180° ÷ n
```

## Explanation

A regular polygon has equal sides and equal angles: equilateral triangle, square, pentagon, hexagon and so on.

### How to use the Regular Polygon Calculator

- **Number of sides**
- **Side length**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The polygon splits into n identical isosceles triangles from the centre, which gives the area and radii.

### Inputs explained

FieldWhat to enterNumber of sidesA numberSide lengthUnits: m, cm, mm, km, in, ft …

### What each result means

- **Area** = [Number of sides] × [Side length]^2 ÷ (4×tan(pi÷[Number of sides]))
- **Perimeter** = [Number of sides]×[Side length]
- **Interior angle** = ([Number of sides] - 2)×180÷[Number of sides]
- **Apothem (inradius)** = [Side length] ÷ (2×tan(pi÷[Number of sides]))
- **Circumradius** = [Side length] ÷ (2×sin(pi÷[Number of sides]))

### Example values

How the main result changes when **Number of sides** changes and everything else stays at the example values above:

Number of sidesArea (m²)36.934.521.45641.577.567.38998.9112179.14

## Worked example

Inputs — Number of sides: 6; Side length: 4 m.

Results — **Area = 41.57 m²**; Perimeter = 24 m; Interior angle = 120 °; Apothem (inradius) = 3.46 m; Circumradius = 4 m.

## Key terms

- **Apothem**: Perpendicular distance from the centre to a side.

## FAQ

**What is an apothem?**
The distance from the centre to the middle of a side.

**What happens as n grows?**
The polygon approaches a circle.

**What formula does the Regular Polygon Calculator use?**
Area = n s² ÷ (4 tan(π ÷ n)).