Moment of inertia of T section calculator for second moment of area, section modulus, radius of gyration, cross section area and centroid calculation of T section beam.

T section is a structural beam with a t shaped cross section and their materials are generally mild steel, aluminum and stainless steel. Manufacturing methods are hot rolling, extrusion and plate welding.

Moment of Inertia of T Section:

Sectional properties of T-beam
Unit System (Quick selection)
Parameter Value
Web height [H]
Flange 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] ---
Minimum 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.

T Section Formula:

Section properties of T-beam
Parameter Symbol Equation
Cross section area A A = Bh + Hb
Area moment of inertia Ixx Ixx = bH(ycog-H/2)2 + bH3/12 + hB(H + h/2 - ycog)2 + h3B/12
Area moment of inertia Iyy Iyy = b3H/12 + B3h/12
Minimum section modulus Sxx Sxx = Ixx/yc
Section modulus Syy Syy = Iyy/xc
Centroid xc xc = B/2
Centroid yc yc= [(H+h/2)hB+H2b/2]/A
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.