Regular Polygon Area Calculator
Area, perimeter, apothem and angles for any n-gon.
Enter your values
Enter the number of sides you are working with.
Enter the side length in units.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Area
- 259.8076 sq units
- Perimeter
- 60
- Apothem (inradius)
- 8.6603
- Circumradius
- 10
- Interior angle
- 120°
- Exterior angle
- 60°
- Sum of interior angles
- 720°
Quick answer
A regular n-gon with side s has area (n·s²) ÷ (4·tan(π/n)), and each interior angle measures (n − 2) × 180° ÷ n.
A = n·s² ÷ (4·tan(π/n))
At a glance
| What it does | Area, perimeter, apothem and angles for any n-gon. |
|---|---|
| Category | Math |
| Inputs needed | Number of sides, Side length |
| Main output | Area |
| Formula | A = n·s² ÷ (4·tan(π/n)) |
| Cost | Free — no sign-up, no download |
How to use the Regular Polygon Area Calculator
- 1Enter how many sides the polygon has.
- 2Enter the length of one side.
- 3Use the apothem when laying out the shape from its centre.
Inputs explained
- Number of sides
- Enter the number of sides you are working with.
- Side length(units)
- Enter the side length in units.
Worked example
Using the values the calculator loads with:
Inputs
- Number of sides6
- Side length10 units
Results
- Area259.8076 sq units
- Perimeter60
- Apothem (inradius)8.6603
- Circumradius10
- Interior angle120°
- Exterior angle60°
- Sum of interior angles720°
Frequently asked questions
What is the apothem?
The perpendicular distance from the centre to the middle of a side — the radius of the inscribed circle.
Does this work for irregular shapes?
No. For irregular polygons use the shoelace formula on the vertex coordinates.
What do I need to enter into the Regular Polygon Area Calculator?
Just 2 values: number of sides, side length. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Regular Polygon Area Calculator work out the answer?
A regular n-gon with side s has area (n·s²) ÷ (4·tan(π/n)), and each interior angle measures (n − 2) × 180° ÷ n. It applies the formula A = n·s² ÷ (4·tan(π/n)) and shows the working so you can check each step by hand.
Is the Regular Polygon Area Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.