Rectangular bars (including square bar) are solid bars (or flats) with rectangle cross section. They are generally produced from stainless steel, carbon steel, alloy steel and aluminum. Manufacturing method for rectangular bars are cold/hot rolling and drawing. Rectangular bars are offered by manufacturers in variety of sizes. Steel rectangular bars are covered by ASTM A108 “Standard Specification for Steel Bar, Carbon and Alloy, Cold-Finished”, A36/A36m “Standard Specification for Carbon Structural Steel” and ASTM A276 “Standard Specification for Stainless Steel Bars and Shapes“ standards.

The following calculator has been developed to calculate the sectional properties of rectangular solid bar.


Sectional properties of solid rectangle
Parameter Symbol Value Unit
Height H
Width B
Length L
Density p

Parameter Symbol Value Unit
Cross section area A ---
Mass M ---
Second moment of area Ixx ---
Second moment of area Iyy ---
Section modulus Sxx ---
Section modulus Syy ---
Radius of gyration rx ---
Radius of gyration ry ---
CoG distance in x direction xcog ---
CoG distance in y direction ycog ---

Note: Use dot "." as decimal separator.



Second Moment of Area: The capacity of a cross-section to resist bending.

Radius of Gyration (Area): The distance from an axis at which the area of a body may be assumed to be concentrated and the second moment area of this configuration equal to the second moment area of the actual body about the same axis.

Section Modulus: The moment of inertia of the area of the cross section of a structural member divided by the distance from the center of gravity to the farthest point of the section; a measure of the flexural strength of the beam.


Link Usage
Simply Supported Beam Deflection Calculation Example An example on calculation of max. deflection, max. shear force, max. bending moment and mid-span slope/deflection of a simply supported beam under multiple point loads and a distributed load.
Rectangular Beam Design for Strength This calculator has been developed to calculate normal stress, shear stress and Von Mises stress on a given cross section of a rectangular solid beam.

List of Equations:

Sectional properties of solid rectangle
Step Parameter/Condition Symbol Equation
1 Cross section area A A = BH
2 Area moment of inertia Ixx Ixx = BH3/12
3 Area moment of inertia Iyy Iyy = HB3/12
4 Section modulus Sxx Sxx = Ixx/ycog
5 Section modulus Syy Syy = Iyy/xcog
6 Center of gravity xcog xcog=B/2
7 Center of gravity ycog ycog=H/2
8 Mass M M = ALρ
9 Radius of gyration r r = (I/A)^0.5
10 Polar moment of inertia J J = Ixx + Iyy


  • Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc., pp 234 - 256