MOMENT OF INERTIA OF RECTANGLE

Moment of inertia of rectangle calculator for area moment of inertia, section modulus, cross section area and radius of gyration calculation of rectangle section.

Steel rectangular bars are covered by ASTM A108 “Standard Specification for Steel Bar, Carbon and Alloy, Cold-Finished”, A36/A36m “Standard Specification for Carbon Structural Steel” and ASTM A276 “Standard Specification for Stainless Steel Bars and Shapes“ standards.

Moment of Inertia of Rectangle Calculator:

INPUT PARAMETERS
Parameter	Value
Height [H]		mm cm m inch ft
Width [B]
Length [L]
Density [p]		g/cm^3 kg/m^3 lb/in^3

Please Wait... 

RESULTS
Parameter	Value
Cross section area [A]	---	mm^2 cm^2 inch^2 ft^2
Mass [M]	---	kg lb
Second moment of area [Ixx]	---	mm^4 cm^4 inch^4 ft^4
Second moment of area [Iyy]	---
Section modulus [Sxx]	---	mm^3 cm^3 inch^3 ft^3
Section modulus [Syy]	---
Radius of gyration [rx]	---	mm cm m inch ft
Radius of gyration [ry]	---
Centroid distance in x direction [xc]	---	mm cm m inch ft
Centroid distance in y direction [yc]	---

Note: Use dot "." as decimal separator.

Definitions:

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.

Moment of Inertia Formula Rectangle:

SOLID RECTANGLE FORMULA
Parameter	Symbol	Equation
Cross section area	A	A = BH
Area moment of inertia	Ixx	Ixx = BH3/12
Area moment of inertia	Iyy	Iyy = HB3/12
Section modulus	Sxx	Sxx = Ixx/yc
Section modulus	Syy	Syy = Iyy/xc
Centroid	xc	xc=B/2
Centroid	yc	yc=H/2
Mass	M	M = ALρ
Radius of gyration	r	r = (I/A)^0.5

Supplements:

• Standard Beam Channel Sizes Dimensions
• Section Properties Calculators
• Simply Supported Beam Deflection Example
• Rectangular Beam Design for Strength

Reference:

• 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.