AREA MOMENT OF INERTIA ROUND BAR

Round bar area and moment of inertia calculator for section modulus, second moment of area, area, radius of gyration and mass of a solid round rod.

Steel round 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. Round bars are generally needed for the production of axles, pins, shafts, etc.

 Round Bar Section Properties Calculator:

INPUT PARAMETERS
Parameter	Value
Diameter [d]		mm cm m inch ft
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]	---
Polar second moment of area [J]	---
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:

Polar Moment of Inertia: A geometric property of the cross section. Measure of ability how a beam resists torsion.

Radius of Gyration (Area): The distance from an axis at which the area of a body may be assumed to be concentrated and at which the second moment area will be equal to the second moment area of the actual body about the same axis. Radius of gyration is equal to the square root of the quotient of the second moment area and the area.

Second Moment of Area: The capacity of a cross-section to resist bending.

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.

Round Bar Formula:

ROUND BAR
Parameter	Symbol	Equation
Cross section area	A	A = πd2/4
Area moment of inertia	Ixx	Ixx = πd4/64
Area moment of inertia	Iyy	Iyy = πd4/64
Section modulus	Sxx	Sxx = 2Ixx/d
Section modulus	Syy	Syy = 2Iyy/d
Centroid	xc	xc=d/2
Centroid	yc	yc=d/2
Mass	M	M = ALρ
Radius of gyration	r	r = (I/A)^0.5
Polar moment of inertia	J	J = Ixx + Iyy

Supplements:

• Standard Beam Channel Sizes Dimensions
• Section Properties Calculators
• Compression of Round Column

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.