Polygon Area Calculator
Calculate the area of Regular or Irregular polygons. Use side lengths or coordinate vertices.
Find the area of any shape. Use the **Regular Mode** if all sides are equal, or **Coordinate Mode** to plot specific vertices on a grid.
Inputs
Drag points on the grid to adjust side lengths! Coordinates update automatically.
Shape Preview (Drag Points)
Properties
O que é Polygon Area Calculator?
Calculating Polygon Areas
For **Regular Polygons** (where all sides and angles are equal), we only need the number of sides and length of one side.
For **Irregular Polygons**, simply knowing the side lengths isn't enough (the shape can flex!). You need coordinates or angles. This tool uses the **Shoelace Formula** to solve for area using coordinates.
Fórmula
Regular Polygon
Area = (n × s²) / (4 × tan(180/n))n = # of sides, s = side length
Shoelace Formula
Area = ½ | Σ(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ) |Sum of cross-products of coords
Exemplo de Cálculo
Example: Pentagon
A regular pentagon with side length 5.
- Inputs: n=5, s=5
- Result Area: ~43.01 square units
Ferramentas Relacionadas
Ferramentas Financeiras Populares
Perguntas Frequentes
Perguntas comuns sobre esta calculadora
Why can't I just use side lengths for irregular polygons?
Think of a square made of 4 hinged sticks. You can squash it into a diamond (rhombus) with the same side lengths but a much smaller area. Without angles or fixed coordinates, the area is not unique!