Polygon - Geometric Properties
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The above polygon property calculator is based on the provided equations and does not account for all mathematical limitations. The calculator has been provided with educational purposes in mind and should be used accordingly. Unit conversion
Need an 
spreadsheet for designing the above shape, click here!
Notation and Units
Metric and Imperial Units
The above formulas may be used with both imperial and metric units. As with all calculations care must be taken to keep consistent units throughout. Examples of units which are typically adopted are outlined below:
Notation
- A = Geometric Area, in2 or mm2
- a = Length of flat section, in or mm
- C = Distance to Centroid, in or mm
- I = Second moment of area, in4 or mm4
- Ji = Polar Moment of Inertia, in4 or mm4
- K = Radius of Gyration, in or mm
- n = Number of flat sides
- P = Perimeter of shape, in or mm
- r = Outer radius of shape, in or mm
- r1 = radius to flat of shape, in or mm
- Z = Elastic Section Modulus, in3 or mm3
Online Polygon Property Calculator
Using the structural engineering calculator located at the top of the page (simply click on the the "show/hide calculator" button) the following properties can be calculated:
- Area of a Polygon
- Perimeter of a Polygon
- Centroid of a Polygon
- Second Moment of Area (or moment of inertia) of a Polygon
- Polar Moment of Inertia of a Polygon
- Radius of Gyration of a Polygon
- Elastic Section Modulus of a Polygon
- Plastic Section Modulus of a Polygon