Round bars are solid bars with round or circular cross section. They are generally produced from stainless steel , carbon steel, alloy and case hardening steel and aluminum. Manufacturing method for round bars are cold/hot rolling and drawing. Round bars are offered by manufacturers in variety of sizes. 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.

The following calculator has been developed to calculate the sectional properties of round bar.


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

Parameter Symbol Value Unit
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 ---
CoG distance in x direction xcog ---
CoG distance in y direction ycog ---

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.

List of Equations:
Sectional properties of solid circle (shaft)
Step Parameter/Condition Symbol Equation
1 Cross section area A A = πd2/4
2 Area moment of inertia Ixx Ixx = πd4/64
3 Area moment of inertia Iyy Iyy = πd4/64
4 Section modulus Sxx Sxx = 2Ixx/d
5 Section modulus Syy Syy = 2Iyy/d
6 Center of gravity xcog xcog=d/2
7 Center of gravity ycog ycog=d/2
8 Mass M M = ALρ
9 Radius of gyration r r = (I/A)^0.5
10 Polar moment of inertia J J = Ixx + Iyy


Link Usage
Compression of Round Column An example about the calculation of allowable load on a compression member. Sectional properties of the member are also calculated.


  • Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc., pp 234 - 256