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Moment of Inertia Calculator for Beam Sections

Welcome to SkyCiv's Free Moment of Inertia Calculator! The following free Section Builder is able to accurately and quickly determine the moment of inertia among others. The following multi-purpose calculator is taken from our Structural Analysis Software and is free to use to do the following:

  • Calculate the Moment of Inertia (I) of a beam section (Second Moment of Area)
  • Calculate the Centroid (C) in the X and Y axis of a beam section
  • Calculate the Statical Moment of Inertia (Q) of a beam section (First Moment of Area)
  • Calculate the Section Modulus (Z) of a beam section
  • Calculate the Torsion Constant (J) of a beam section

The Beam Section Calculator is able to find the moment of inertia for a hollow section, circular section, triangular, I-Beam, T-Beam and L-Sections. The dynamic section drawer will also show you a graphical representation of your section.

Free Structural Analysis Software

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Select Units:

Notation Value Unit
A - -
Iz - -
Iy - -
Izp - -
Iyp - -
αp - -
Cz - -
Cy - -
Qz - -
Qy - -
Zz - -
Zy - -
J - -

  • David Wimberley

    I’m a first time user and fan of what you’re doing, but I have a constructive suggestion. It seems to me intrinsically confusing to have two rectangular cross-sections in your example, one of which is higher than it is wide, and the other wider than it is high. It would be much less confusing to be able to input your data into a single rectangle. Thanks for hearing me out.

    • Hi David,

      I completely agree. This is why in our new section builder you just need to specify the outer width and depth with a thickness. If you sign up for free account, you can access it by clicking ‘SB’ in the left menu:

      • David Wimberley

        OK. Did so. Thanks.


    can anyone differentiate between moment of inertia of two rectangular beams, with and without holes over it.

  • Anitha G

    am designing triangular cantilever beam, how to calculate stress, displacement, moment inertia, and theoretical i have to prove, plz suggest me and give some material to understanding.

  • Shaun Murrin

    This is a tutorial question I’m struggling a bit which axis in to vase the I value in..”Based on calculations it has been determined that a universal steel column must have a minimum value of I of 38748 cm4. Select a column suitable for this scenario showing clearly why you have selected that particular column” .

  • Chris Webb

    I hate the moor

  • jamsheed sajid

    wow a nice and great work done by you. being a mechanical engineering student i think now i have found all what i need through out degree. thanks a lot for such a great work. i salute you

  • Gokul Kgs

    Can anyone help me to find out the moment of inertia for this type of I-Profile.
    I need a little detail explanation.

    • Hi Gokul. Wow this is a complex one! The first step is always finding the centroid of the area as that will tell you where the neutral axes are. Then you need to divide the area into different sections. Both of these steps are explained in our tutorials: skyciv.com/tutorials

      This is a complex section though – it will probably take 1+ hours by hand. Hopefully in future we can add custom section shapes in future.

      • Gokul

        Thanks for your reply.
        i just want to know that how to consider the curves present in it. Is there any way to find easily like software……..

        • mecheng

          Maybe a bit too late to be helpful, but I’d just sketch it in Solidworks or similar and use the built in ‘evaluate section’ function. Any proper CAD system should have this function. Google will help you a long way on how to do it 😉

        • Muthamizhselvan Vijayan

          Hi gokul, better you extrude this profile in creo parametric and go for mass properties..

    • Pape Modou Fall

      you can use autocad logiciel

      1-at first you drax this section
      2-you click left “Region” and selection all the section
      3-finaly , you click left again for select “Propmeca”, you select your region

      and you have ( Iy, Iz, Go, A, P)
      if you draw it at dwg, I can do it for you

    • HollywoodF1

      Check with the Aluminum Design Manual (I’m assuming this is Aluminum.) The section properties are limited by the strength of the elements of the section. SAP 2000 has a tool where it will calculate the section properties of shapes you import from AutoCAD.

  • Raghda Al Rashii

    I don’t get how did you find Iz?

  • It’s not easy to find such perfectly written information on this topic,great work,thanks for sharing….!

  • Roland

    Why does it give Iz and Iy rotated for a L-beam? What if I want the area moment of inertia about the vertical and horizontal axes?

    • L-sections and some channel sections are asymmetric in both the horizontal and vertical axes. So when a load is applied the member actually twists (see the image from SkyCiv Structural 3D renderer – only a vertical load is applied yet there is displacement in two directions). The Iz and Iy values shown are about the principal (rotated) axes. Perhaps in the future we can provide the values about the vertical and horizontal axes too. Thanks for the suggestion.

      • travis

        beautiful pic! (:

        • travis


  • Al

    section modulus in the ‘Z’ and ‘Y’ axis should not be the same value?

    • Which section are you referring too so we can check it? If it is symmetric then it would be the same value.

  • Manuel Sierra

    Muy útil, gracias mil

  • Guilherme Henrique

    this is very useful, but it’s missing a geometric composition tool. Thanks anyway.

  • Zia Ul Islam

    Hey Paul, Thank you so much. Can you please put up ” Z ” shaped cross sections in there as well ? Would be greatly appreciated :)

    • Hi Zia, I really hope in the near future we can add many many more sections :) including the Z-section!

  • Tarek J. Ammar

    Would be great if you can include calculations for notched beams ( For connections’ purposes)

    • Hi Tarek. Thanks for the feedback although I’m not 100% sure what you mean – could you please elaborate or provide an example? Thanks.

      • Tarek J. Ammar

        Anytime. Well mostly in designing connections for beams-to-beams/columns you’re required to notch same-sized beams at the end so they can be connected to the web so I section becomes a notched T section. Furthermore its necessary to find the moment of inertia and stresses onto that beam

  • Bak

    hi. what about a reversed t beam ? Thanks.

    • Hi Bak. If you invert the T-beam the results would be identical except for the values of the Centroid since they are always measured from the bottom left of the section. Hope that helps!

  • Vincent

    Is it possible to get the equation for Ix and Iy for the T-Beam?

    • Hi Vincent. We’ll be adding the formulae for most results in the near future. Sorry but the T-beam is very complex to type out so you’re going to have to wait. Sorry about that.

  • lir

    The origion of axis system should be at Center of mass, otherwise results are not correct.

    • Thanks for letting us know. This has been fixed.

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