Wide Flange I Beam Sizes Calculator has been developed according to ASTM A 6/A 6M standard to give basic dimensions and section properties of wide flange I beam. Section properties which are calculated by the calculator are second area moment of inertia, section modulus, radius of gyration.  These sectional properties are calculation results and there may be some minor differences with the values given by structural steel suppliers.

The wide flange I beam (W shape) is a structural steel shape with I (or H) form. Top and bottom plates of a I beam are named as flanges and the vertical plate which connects the flanges is named as web. In wide flange I beams, flanges are nearly parallel to each other.

Wide flange I beams are most commonly used structural steel shape in construction works. Materials of wide flange beams are generally structural steels such as A36, A572, A588 and A992.

The designation of the wide flange I beam gives information about the width and weight per unit length. For example W12 X 96 means 12 inches depth and 96 pounds per foot weight per unit length. Depth values are generally approximate. For W12 x 96, actual depth value is 12.71. Therefore the actual depth value is a dimension that must be checked while designing a structural steel system.

The dimensions of the standard wide flange I beams are defined in the annex of ASTM A 6/A 6M standard.

This calculator covers sizes of wide flange I beams which are frequently used in steel structures. It shall be referred to products of steel suppliers if desired wide flange I beam size doesn't exist in this calculator.


Unit System
Nominal Depth Weight in pounds per foot


Structural Steel Shapes - W Shape
Parameter Symbol Value Unit
Designation --- --- ---
Weight per unit length W --- lb/ft
Cross section area A --- in^2
Depth d --- in
Web thickness tw ---
Flange width bf ---
Flange thickness tf ---
Fillet radius * R ---
Second moment of area Ixx --- in^4
Second moment of area Iyy ---
Section modulus Sxx --- in^3
Section modulus Syy ---
Radius of gyration rx --- in
Radius of gyration ry ---

Note: Use dot "." as decimal separator.

Note: * The fillet radius , which is used to calculate the sectional properties (Ixx, Iyy, Sxx..) of the structural wide flange beam, is a calculated value to have an area  which equals to the area value that is given in the ASTM A6 / A6M. Fillet radius may vary from structural steel fabricator to fabricator but the effect of this change on sectional properties will be minor.


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.

List of Equations:

Sectional properties of W-shape I-beam
Step Parameter/Condition Symbol Equation
1 Flange inner distance H H=d-2tf
2 Cross section area A A = 2bftf + Htw + Afillets
3 Area moment of inertia Ixx Ixx = H3tw/12 + 2[tf3bf/12 + tfbf(H+tf)2/4]+ Ixx_fillets
4 Area moment of inertia Iyy Iyy = tw3H/12 + 2(bf3tf/12) + + Iyy_fillets
5 Section modulus Sxx Sxx = 2Ixx/(d)
6 Section modulus Syy Syy = 2Iyy/bf
7 Radius of gyration r r = (I/A)^0.5


  • Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc., pp 2594 - 2597
  • A 6/A 6M - 05a , Standard Specification for General Requirements for Rolled Structural Steel Bars, Plates, Shapes, and Sheet Piling
  • Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGraw-Hill