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.

Beam Cross Section	I Beam Hollow Rectangle Rectangle C Channel T Section Circular Hollow Section Round Bar Angle
Unit System (Quick selection)	Metric Inch
INPUT PARAMETERS
Parameter	Value
Flange-flange inner face height [H]		mm cm m inch ft
Width [B]
Flange thickness [h]
Web thickness [b]

Please Wait... 

RESULTS
Parameter	Value
Second moment of area [Ixx]	---	mm^4 inch^4 cm^4 ft^4
Second moment of area [Iyy]	---

Note: Use dot "." as decimal separator.

Second Moment of Area Formula:

I Beam Area Moment of Inertia Formula
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
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
Parameter	Equation
Area moment of inertia	Ixx = BH3/12
Area moment of inertia	Iyy = HB3/12

C Channel Area Moment of Inertia Formula
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
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
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
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
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))

Supplements:

• Standard Beam Channel Sizes Dimensions
• Section Properties Calculators

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.