About this calculator
The Polygon Calculator finds area, perimeter, interior angle, exterior angle, and interior angle sum for regular polygons. It works for common shapes such as triangles, squares, pentagons, hexagons, octagons, decagons, and dodecagons.
polygon calculator method
For a regular polygon, every side and angle is equal. The calculator uses the side length and number of sides to calculate perimeter, area, and angles.
- Perimeter = n x s
- Area = (n x s^2) / (4 x tan(pi / n))
- Interior angle = (n - 2) x 180 / n
- Exterior angle = 360 / n
- Interior angle sum = (n - 2) x 180
How to use the polygon calculator
- Enter the number of sides from 3 to 20.
- Enter the side length.
- Multiply sides by side length for perimeter.
- Use the regular polygon area formula.
- Calculate interior and exterior angles.
- Check the shape name for common side counts.
Worked examples
Regular hexagon
Input: n = 6, s = 5
Calculation: P = 6 x 5
Result: Perimeter 30
Square
Input: n = 4, s = 10
Calculation: Area = (4 x 10^2) / (4 x tan(pi/4))
Result: Area 100
Regular polygons only
The area and angle formulas assume a regular polygon. If the sides or angles are unequal, split the shape into triangles or rectangles and calculate each part separately.
Practical geometry checks
- Use one unit system
- Keep all lengths in the same unit before calculating. Mixing centimetres, metres, inches, or feet in the same formula will produce misleading results.
- Perimeter vs area
- Perimeter is a distance around the outside. Area is the amount of flat space inside a shape. Surface area is the total outside covering of a 3D shape.
- Rounded answers
- Pi, square roots, and trigonometric values are often irrational, so decimal answers are approximations. Keep extra decimal places until the final result.
Edge cases
- Zero or negative dimensions do not describe a real physical shape.
- Regular polygon formulas assume all sides and angles are equal.
- Circle and ellipse formulas use pi, so most decimal answers are rounded.
- A trapezoid/trapezium perimeter needs all four side lengths, not just the parallel sides and height.
Limitations
This calculator is for educational and planning use. For construction, manufacturing, surveying, engineering, or safety-critical work, confirm dimensions, tolerances, and rounding rules with the appropriate professional method or specification.
Frequently asked questions
What units should I enter?
Use any length unit you like, but keep every length in the same unit. If you enter metres, area is in square metres and surface area is also in square metres.
Why are some answers approximate?
Calculations involving pi, square roots, or curved shapes often produce irrational numbers. The calculator rounds the displayed decimal result.
What is the difference between area and surface area?
Area measures a flat 2D region. Surface area measures the total outside area of a 3D object.
Can I use these calculators for homework?
Yes. They are useful for checking answers and understanding formulas, but you should still show the working required by your class or exam.
Do regular polygon formulas work for irregular polygons?
No. Regular polygon formulas assume equal sides and equal angles. Irregular polygons usually need to be split into simpler shapes.
Related calculators
- Hexagon Calculator
- Perimeter Calculator
- Area Calculator