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:

Sectional properties of solid circle (shaft)
Parameter Value
Diameter [d]
Length [L]
Density [p]

Parameter Value
Cross section area [A] ---
Mass [M] ---
Second moment of area [Ixx] ---
Second moment of area [Iyy] ---
Polar second moment of area [J] ---
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.



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:

Sectional properties of solid circle (shaft)
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



  • 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.