Rotated Rectangle - Geometric Properties

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StructX Calculator
Geometric Property Calculator
Plate design formula Side, a:

Side, b:

Angle, Φ:




mm

mm

degrees
Area, A: mm2
Perimeter, P: mm
Centroid, Cx: mm
Centroid, Cy: mm
Second Moment of Area, Ix: mm4
Polar Moment of Inertia, Jz: mm4
Radius of Gyration, Kx: mm
Elastic Section Modulus, Zx: mm3
   

The above rotated rectangle 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 Rotated Rectangle

Need an excel 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 shape, in or mm
  • b = Width of shape, 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
  • P = Perimeter of shape, in or mm
  • Z = Elastic Section Modulus, in3 or mm3
  • ø = Angle of rotation of rectangle, radians

Online Rotated Rectangle 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 Rotated Rectangle
  • Perimeter of a Rotated Rectangle
  • Centroid of a Rotated Rectangle
  • Second Moment of Area (or moment of inertia) of a Rotated Rectangle
  • Polar Moment of Inertia of a Rotated Rectangle
  • Radius of Gyration of a Rotated Rectangle
  • Elastic Section Modulus of a Rotated Rectangle
  • Plastic Section Modulus of a Rotated Rectangle