Calculator Input
Example Data Table
Example irregular pentagon coordinates are shown below. This sample produces an area of 21 square units.
| Vertex | X | Y |
|---|---|---|
| P1 | 0 | 0 |
| P2 | 4 | 0 |
| P3 | 5 | 3 |
| P4 | 2 | 5 |
| P5 | -1 | 3 |
Formula Used
1) Shoelace formula for coordinate vertices
For points listed in order around the boundary:
A = 1/2 × |Σ(xiyi+1 − yixi+1)|
2) Regular polygon area from side length
A = n × s² / (4 × tan(π / n))
3) Regular polygon area from apothem and perimeter
A = (1/2) × a × P
Here, n is the number of sides, s is side length, a is apothem, and P is perimeter.
How to Use This Calculator
- Choose Vertices from coordinates for any irregular polygon or Regular polygon for equal-sided, equal-angled shapes.
- Enter your unit label and preferred decimal precision.
- For coordinate mode, type one vertex per line using x and y values in boundary order.
- For regular mode, enter the number of sides, choose a known dimension, and provide its value.
- Press Calculate Polygon Area to show the result above the form.
- Review the area, perimeter, derived measures, graph, and optional report downloads.
Frequently Asked Questions
1) What is the best method for an irregular polygon?
Use the coordinate mode. Enter each vertex in boundary order, and the calculator applies the shoelace formula to find the enclosed area accurately.
2) Does vertex order matter?
Yes. Enter vertices around the shape in either clockwise or counterclockwise order. Random order can create crossing edges and produce the wrong area.
3) Can I use negative coordinates?
Yes. Negative x or y values work normally. The calculator uses the full coordinate list and still returns a positive area magnitude.
4) What if my polygon is regular?
Choose regular polygon mode. Enter the number of sides and one known measure, such as side length, apothem, circumradius, or perimeter.
5) Why does the calculator show perimeter too?
Perimeter helps with design checks, fencing, framing, and comparison tasks. It is often useful alongside area when planning material or boundary length.
6) What units should I enter?
Use any consistent linear unit, such as cm, m, ft, or in. Area is then reported automatically in squared units, like cm² or ft².
7) Why is the graph helpful?
The graph helps you confirm the plotted shape matches your intended polygon. It is especially useful for spotting incorrect vertex order or unexpected symmetry.
8) Can I save the results?
Yes. After calculation, use the CSV button for spreadsheet-friendly output or the PDF button for a quick printable summary report.