Round hollow structural sections are metal profiles with circular tube section. They are also known as round steel tubes. ASTM A500 is the most common steel specification for hollow structural section in North America. This specification is for cold formed welded and seamless carbon steel tubing in round, square and rectangular shapes. ASTM A501 is another standard for hot formed steel tubing. Hollow round sections are used in structural applications.

The following calculator has been developed to calculate the sectional properties of structural hollow round sections (tubes).


Sectional properties of hollow circle (shaft)
Parameter Symbol Value Unit
Outer diameter (d) d
Inner diameter (d1) d1
Length (L) L
Density (p) 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 capacity of a cross-section to resist bending.

Second Moment of 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.


Link Usage
HSS Steel Tube Sizes and Dimensions This page gives sizes, dimensions and section properties of HSS steel tubes (round hollow structural sections) per Steel Construction Manual.
Pipes (Std, x-Strong, xx-Strong) - Dimensions and Properties This page gives sizes, dimensions and section properties of standard, extra strong and double-extra strong pipes per Steel Construction Manual.

List of Equations:

Sectional properties of hollow circle (shaft)
Step Parameter/Condition Symbol Equation
1 Cross section area A A = πd2/4 - πd12/4
2 Area moment of inertia Ixx Ixx = πd4/64 - πd14/64
3 Area moment of inertia Iyy Iyy = πd4/64 - πd14/64
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


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