Regular Polygon Area Calculator
Area, perimeter, apothem and angles for any n-gon.
Reviewed by James Whitfield · How we check our maths
Your values
ⓘ Live results
Results
- 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.
The formula
A = n·s² ÷ (4·tan(π/n))
Worked example
Worked example
Using the values the calculator loads with.
Inputs
- Number of sides6
- Side length10 units
Result
- Area259.8076 sq units
- Perimeter60
- Apothem (inradius)8.6603
- Circumradius10
- Interior angle120°
- Exterior angle60°
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.
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.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error