SECOND MOMENT OF AREA (AREA MOMENT OF INERTIA) CALCULATOR

Second Moment of Area Calculator for I beam, T section, rectangle, c channel, hollow rectangle, round bar and unequal angle.

Second Moment of Area is defined as the capacity of a cross-section to resist bending.

Sectional properties of I-beam
Beam Cross Section
Unit System (Quick selection)
INPUT PARAMETERS
Parameter Value
Flange-flange inner face height [H]
Width [B]
Flange thickness [h]
Web thickness [b]

RESULTS
Parameter Value
Second moment of area [Ixx] ---
Second moment of area [Iyy] ---

Note: Use dot "." as decimal separator.

 

Second Moment of Area Formula:

I Beam Area Moment of Inertia Formula
Sectional properties of I-beam
Parameter Equation
Area moment of inertia Ixx = H3b/12 + 2[h3B/12 + hB(H+h)2/4]
Area moment of inertia Iyy = b3H/12 + 2(B3h/12)
Hollow Rectangle Area Moment of Inertia Formula
Sectional properties of hollow rectangle
Parameter Equation
Area moment of inertia Ixx = BH3/12 - bh3/12
Area moment of inertia Iyy = HB3/12 - hb3/12
Rectangle Area Moment of Inertia Formula
Sectional properties of hollow rectangle
Parameter Equation
Area moment of inertia Ixx = BH3/12
Area moment of inertia Iyy = HB3/12
C Channel Area Moment of Inertia Formula
Sectional properties of C-beam
Parameter Equation
Area moment of inertia Ixx = H3b/12 + 2[h3B/12 + hB(h+H)2/4]
Area moment of inertia Iyy = b3H/12 + bH(xc-b/2)2+ 2B3h/12+ 2Bh(xc - B/2)2
Centroid distance xc = (2hB2/2 + b2H/2)/A
Centroid distance yc= H/2 + h
T Section Area Moment of Inertia Formula
Section properties of T-beam
Symbol Equation
Area moment of inertia Ixx = bH(yc-H/2)2 + bH3/12 + hB(H + h/2 - yc)2 + h3B/12
Area moment of inertia Iyy = b3H/12 + B3h/12
Centroid distance xc = B/2
Centroid distance yc= [(H+h/2)hB+H2b/2]/A
Hollow Circle Area Moment of Inertia Formula
Section properties of hollow circle (shaft)
Parameter Equation
Area moment of inertia Ixx = πd4/64 - πd14/64
Area moment of inertia Iyy = πd4/64 - πd14/64
Round Bar Area Moment of Inertia Formula
Section properties of round bar
Parameter Equation
Area moment of inertia Ixx = πd4/64
Area moment of inertia Iyy = πd4/64
Angle with Unequal Legs Area Moment of Inertia Formula
Sectional properties of angle with unequal legs
Symbol Equation
Area moment of inertia Ixx = 1/3*[bd3 - (b-t) * (d-t)3] - A * (d - yc)2
Area moment of inertia Iyy = 1/3*[db3 - (d-t) * (b-t)3] - A * (b - xc)2
Centroid distance xc=(b2+dt-t2)/(2*(b+d-t))
Centroid distance yc=(d2+bt-t2)/(2*(b+d-t))

Reference:

  • 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.