I beam moment of inertia calculator for calculation of second moment of area (moment of inertia) of I beam, section modulus, radius of gyration, cross section area and centroid.

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.

Sectional properties of I-beam
Unit System (Quick selection)
Parameter Value
Flange-flange inner face height [H]
Width [B]
Flange thickness [h]
Web thickness [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] ---
Centroid distance in x direction [xc] ---
Centroid distance in y direction [yc] ---

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.

I Meam Moment of Inertia Formula and et al.:

Sectional properties of I-beam
Parameter Symbol Equation
Cross section area A A = 2Bh + Hb
Area moment of inertia Ixx Ixx = H3b/12 + 2[h3B/12 + hB(H+h)2/4]
Area moment of inertia Iyy Iyy = b3H/12 + 2(B3h/12)
Section modulus Sxx Sxx = 2Ixx/(H + 2h)
Section modulus Syy Syy = 2Iyy/B
Centroid xc xc=B/2
Centroid yc yc=H/2 + h
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.
  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc.