Issue 1 V1.07
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Circle Sector - Geometric Properties

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StructX Calculator
Geometric Property Calculator
Plate design formula Radius, r:

Angle, θ


mm

degrees
Area, A: mm2
Perimeter, P: mm
Centroid, Cx: mm
Centroid, Cy: mm
Second Moment of Area, Ix: mm4
Second Moment of Area, Iy: mm4
Second Moment of Area, Ix1: mm4
Second Moment of Area, Iy1: mm4
Polar Moment of Inertia, Jz: mm4
Polar Moment of Inertia, Jz1: mm4
Radius of Gyration, Kx: mm
Radius of Gyration, Ky: mm
Radius of Gyration, Kx1: mm
Radius of Gyration, Ky1: mm
Elastic Section Modulus, Z: mm3
   

The above circle sector 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

Geometric Properties of a Circle Sector

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
  • 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
  • P = Perimeter of shape, in or mm
  • Z = Elastic Section Modulus, in3 or mm3

Online Circle Sector 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:

  • Calculate the Area of a Circle Sector
  • Calculate the Perimeter of a Circle Sector
  • Calculate the Centroid of a Circle Sector
  • Calculate the Second Moment of Area (or moment of inertia) of a Circle Sector
  • Calculate the Polar Moment of Inertia of a Circle Sector
  • Calculate the Radius of Gyration of a Circle Sector
  • Calculate the Elastic Section Modulus of a Circle Sector
  • Calculate the Plastic Section Modulus of a Circle Sector