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.

Rectangular section properties calculator finds area moment of inertia, section modulus, cross section area and radius of gyration of solid rectangular section.

Rectangular Section Properties Calculator:

Sectional properties of solid rectangle
Parameter Value
Height [H]
Width [B]
Length [L]
Density [p]

Parameter Value
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
Parameter Symbol Equation
Cross section area A A = BH
Area moment of inertia Ixx Ixx = BH3/12
Area moment of inertia Iyy Iyy = HB3/12
Section modulus Sxx Sxx = Ixx/ycog
Section modulus Syy Syy = Iyy/xcog
Center of gravity xcog xcog=B/2
Center of gravity ycog ycog=H/2
Mass M M = ALρ
Radius of gyration r r = (I/A)^0.5


  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc., pp 226-235 .
  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc., pp 234-256.