Beam is a structural element used in construction works to support loads and moments. Beams are generally manufactured from steel and aluminum. Different shapes and dimensions are supplied by beam suppliers.

I beam is a type of beam often used in trusses in buildings. I beam is generally manufactured from structural steels with hot and cold rolling or welding processes. Top and bottom plates of a I beam are named as flanges and the vertical plate which connects the flanges is named as web. Different dimensions of I beam exist in the market and can be supplied by the beam suppliers. Due to its shape, I beam has high moment of inertia and stiffness which makes it resistant to bending moments. The web provides resistance against shear forces. These beams are not resistant to torsional loading (twisting) and they shall not used in the cases where torsion is dominant.

The following calculator has been developed to calculate the sectional properties of structural I beams.


Sectional properties of I-beam
Unit System (Quick selection)
Parameter Symbol Value Unit
Flange-flange inner face height H
Width B
Flange thickness h
Web thickness 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.

List of Equations:

Sectional properties of I-beam
Step Parameter/Condition Symbol Equation
1 Cross section area A A = 2Bh + Hb
2 Area moment of inertia Ixx Ixx = H3b/12 + 2[h3B/12 + hB(H+h)2/4]
3 Area moment of inertia Iyy Iyy = b3H/12 + 2(B3h/12)
4 Section modulus Sxx Sxx = 2Ixx/(H + 2h)
5 Section modulus Syy Syy = 2Iyy/B
6 Center of gravity xcog xcog=B/2
7 Center of gravity ycog ycog=H/2 + h
8 Mass M M = ALρ
9 Radius of gyration r r = (I/A)^0.5
10 Polar moment of inertia J J = Ixx + Iyy


Link Usage
Eccentric Compression Load On I-Beam An example about the calculation of  factor of safety of a compression member which is loaded eccentrically. Sectional properties of the member are also calculated.


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