area of a polygon calculator

What This Polygon Area Tool Does

This calculator helps you find the area of many common polygon shapes quickly and accurately. You can use it in two ways:

• Regular polygon mode: best for shapes like equilateral triangles, squares, pentagons, hexagons, and other polygons where all sides are equal.
• Coordinate polygon mode: best when you know each vertex location on an x-y plane, such as in surveying, CAD, map work, physics, or geometry homework.

The output is given in square units. For example, if your side lengths are in meters, your area will be in square meters (m²).

Method 1: Area of a Regular Polygon

For a regular polygon with n sides and side length s, the area formula is:

This formula works only when the polygon is regular (equal side lengths and equal angles).

When to use regular mode

• You know the number of sides.
• Each side has the same length.
• You need a fast area and perimeter estimate.

Method 2: Area from Coordinates (Shoelace Formula)

If you know the vertex coordinates in order around the shape, use the Shoelace Formula:

This method is very flexible and works for irregular polygons, as long as the edges do not cross each other.

How to enter coordinates correctly

• Enter vertices in clockwise or counterclockwise order.
• Do not skip around between non-adjacent points.
• Use consistent units for all x and y values.

Quick Examples

Example 1: Regular hexagon

If a hexagon has 6 sides and each side is 4 units:

So the area is approximately 41.569 square units.

Example 2: Rectangle from coordinates

Points: (0,0), (8,0), (8,3), (0,3). The shoelace method returns an area of 24 square units.

Common Mistakes to Avoid

• Using regular polygon mode for a shape that is not truly regular.
• Entering fewer than 3 vertices.
• Mixing units (for example, x in feet and y in meters).
• Entering coordinate points out of perimeter order.

Why Polygon Area Matters

Area calculations for polygons are used in architecture, civil engineering, construction planning, GIS mapping, graphic design, and data visualization. A reliable polygon area calculator saves time and reduces manual arithmetic errors.

FAQ

Does this work for concave polygons?

Yes, the coordinate method works for many concave polygons, provided the polygon is simple (its edges do not cross).

Can I use decimal values?

Absolutely. Both methods support decimal inputs for precision.

What if the result is zero?

A zero area usually means your points are collinear or duplicated in a way that collapses the shape.