Regular Polygon Calculator
Find the area, perimeter, apothem and angles of any regular polygon from its number of sides and side length.
Area
41.56921938
- Perimeter
- 24
- Apothem (inradius)
- 3.464101615
- Circumradius
- 4
- Interior angle
- 120°
- Exterior angle
- 60°
- Diagonals
- 9
Show the work
Half the angle each side spans at the center
θ = 180° ÷ n
180° ÷ 6 = 30°
Area
A = n × s to the power of 2 ÷ (4 × tan θ)
6 × 4 to the power of 2 ÷ (4 × tan 30°) = 41.56921938
How it works
Area = n s² ÷ (4 tan(π/n)); apothem = s ÷ (2 tan(π/n)); circumradius = s ÷ (2 sin(π/n)); interior angle = (n − 2) × 180° ÷ n
Questions
- How does the regular polygon calculator work?
- Area = n s² ÷ (4 tan(π/n)); apothem = s ÷ (2 tan(π/n)); circumradius = s ÷ (2 sin(π/n)); interior angle = (n − 2) × 180° ÷ n.
- What do I need to enter?
- Number of sides, Side length, Units. Optional fields can be left blank.
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