How to use a polygon area calculator
Start with the shape you have. Regular polygon uses a side count and one side length, while Coordinates uses one ordered x,y pair per line. After you choose a Unit, Calculate shows area, perimeter, and the steps used.
- Choose Regular polygon for equal sides and angles, or choose Coordinates for vertices.
- Enter Number of sides (n) and Side length (s), or enter one pair per line in Vertex coordinates.
- Select Unit in the active input panel.
- Click Calculate and inspect Result and Formula & steps.
- Click Copy result or Download result (.txt) to reuse the text. Reset empties both input modes, selects Regular polygon, and returns both units to meters.
Polygon area calculator for regular polygons
Choose Regular polygon when every side and interior angle is equal. Enter a whole number between 3 and 200 in Number of sides (n), a positive value in Side length (s), and a length in Unit. Result includes area, perimeter, apothem, circumradius, and interior angle.
Number of sides (n): 6
Side length (s): 2
Unit: Meters (m)
Area: 10.392305 m²
Perimeter: 12 mThe regular-polygon calculation uses A = 1/2 x P x a. Formula & steps shows the apothem and perimeter, plus a conversion step when the selected unit is not meters.
Area of a polygon with coordinates
Choose Coordinates when the corners are known. Enter 3 to 200 lines in Vertex coordinates. Each line needs exactly one x,y pair, and the points must follow the boundary in clockwise or counter-clockwise order.
0,0
4,0
4,3
0,3
Area: 12 m²
Perimeter: 14 mThis mode applies the shoelace formula in the order entered. It calculates perimeter by adding the straight-line distances between consecutive vertices, including the last point back to the first. The code does not detect or correct self-intersecting orders. Collinear points produce an error because they enclose no area.
Units and input limits
- Unit supports millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles.
- Area uses the squared form of the selected unit, while perimeter uses the length unit.
- Side length (s) and each coordinate must be within
1e12in absolute value. - Side length (s) accepts positive decimals. Coordinate values may be negative decimals, but each line still needs exactly two comma-separated values.
The calculation runs in the browser from the values entered here, and the script makes no request with those values. The result text can be copied or saved as polygon-area-calculator-result.txt. If copying fails, the page leaves the text available for manual selection.
Where polygon area calculations come up
For a regular-hexagon exercise, enter the side count and side length, then check the displayed apothem alongside the other results. For a parcel outline, enter each corner in boundary order and review the area and perimeter.
A cutout with four or more corners can use the coordinate mode. The plain-text result can then go into project notes.
When another math calculator fits better
Browse Math Calculators for an equation, fraction, sequence, matrix, vector, or another calculation. Use Circle Area Calculator for a circle's area, radius, diameter, or circumference. Use Triangle Area Calculator when the shape is a triangle and the known measurements are base and height, three sides, or three coordinate points. Geometry Calculator covers slope, distance, midpoint, triangle area, circle measurements, polygon area, and common solid measurements.
Frequently asked questions
How do I calculate the area of a regular polygon?
Choose Regular polygon, enter the side count and positive side length, and click Calculate. The calculator uses the perimeter and apothem in A = 1/2 x P x a.
How do I find the area of a polygon from coordinates?
Choose Coordinates and enter one ordered x,y pair per line in Vertex coordinates. The calculator applies the shoelace formula and reports area and perimeter in the selected unit.
Do polygon coordinates need to be in order?
Yes. Enter vertices around the boundary in a consistent clockwise or counter-clockwise order. The code does not detect or fix self-intersecting orders.
What units can I use for polygon area?
You can choose millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles. Area is displayed in the squared version of the selected unit.
What does Reset clear in the polygon area calculator?
Reset clears both input modes, restores meters, selects Regular polygon, clears errors, and hides the current result.